C ALGORITHM 731, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 20, NO. 2, JUNE, 1994, PP. 194-214. C####################################################################### C C Text material TOMS submission `A Moving-Grid Interface for Systems of C One-Dimensional Time-Dependent Partial Differential Equations' by C J.G. Blom and P.A. Zegeling. C C Contains, separated by a C######## line, the following files: C ------------------------------------------------------------ C SRCFIL : description of contents of source code file C DRVDOC : documentation of the test program which shows the use C of the moving-grid interface in a DASSL environment. C MIFDOC : software documentation of the moving-grid interface itself. C RESBAK : RESULT file from single precision version C for the first example problem C RUNBAK : RUNINF file from single precision version C for the first example problem C RESCYL : RESULT file from single precision version C for the second example problem C RUNCYL : RUNINF file from single precision version C for the second example problem C RESDSH : RESULT file from single precision version !!!!!!!!!!!!!!!!!! C for the third example problem !!! TAU = 1E-3 !!! C RUNDSH : RUNINF file from single precision version !!! in driver !!! C for the third example problem !!!!!!!!!!!!!!!!!! C RESBAK : RESULT file from double precision version C for the first example problem C RUNBAK : RUNINF file from double precision version C for the first example problem C RESCYL : RESULT file from double precision version C for the second example problem C RUNCYL : RUNINF file from double precision version C for the second example problem C RESDSH : RESULT file from double precision version !!!!!!!!!!!!!!!!!! C for the third example problem !!! TAU = 1E-3 !!! C RUNDSH : RUNINF file from double precision version !!! in driver !!! C for the third example problem !!!!!!!!!!!!!!!!!! C C NB. The single precision results were obtained on a Cray Y-MP and C the double precision results on an SGI Indigo. C####################################################################### C C SRCFIL : description of contents of source code file C C####################################################################### C C*********************************************************************** C C Single Precision files C C*********************************************************************** C C PRBBAK : problem dependent routines for first example problem C PRBCYL : problem dependent routines for second example problem C PRBDSH : problem dependent routines for third example problem C (Burgers' equation) C DRIVER : test program to use the moving-grid interface in a DASSL C environment C SPMDIF : moving-grid interface routines C MACHAR : MACHAR routine from W.J. Cody C (available from Netlib: send machar from elefunt) C SDASSL : DASSL DAE integrator from L.R. Petzold C (available from Netlib: send sdassl from ode) C NB. DASSL needs the following files: C DASUSE : contains the routine C I1MACH to get the standard error message unit (6). C (also available from Netlib: send i1mach from core) C R1MACH to determine machine precision, uses value determined C by MACHAR C (also available from Netlib: send r1mach from core) C and the dummies for the routines SGEFA and SGESL from LINPACK C (available from Netlib: send sgefa/sgesl from linpack) C DASLIP : LINPACK routines needed by DASSL C (available from Netlib: send sgbfa/sgbsl from linpack) C C*********************************************************************** C C Double Precision files C C*********************************************************************** C C PRBBAK : problem dependent routines for first example problem C PRBCYL : problem dependent routines for second example problem C PRBDSH : problem dependent routines for third example problem C (Burgers' equation) C DRIVER : test program to use the moving-grid interface in a DASSL C environment C SPMDIF : moving-grid interface routines C MACHAR : MACHAR routine from W.J. Cody C (available from Netlib: send machar from elefunt) C DDASSL : DASSL DAE integrator from L.R. Petzold C (available from Netlib: send ddassl from ode) C NB. DASSL needs the following files: C DASUSE : contains the routine C I1MACH to get the standard error message unit (6). C (also available from Netlib: send i1mach from core) C D1MACH to determine machine precision, uses value determined C by MACHAR C (also available from Netlib: send d1mach from core) C and the dummies for the routines DGEFA and DGESL from LINPACK C (available from Netlib: send dgefa/dgesl from linpack) C DASLIP : LINPACK routines needed by DASSL C (available from Netlib: send dgbfa/dgbsl from linpack) C C####################################################################### C C DRVDOC : documentation of the test program which shows the use C of the moving-grid interface in a DASSL environment. C C####################################################################### C C Description of DRIVER: C --------------------- C Main program MoL adaptive grid interface for DASSL C Calls problem initializer, C Initializes DASSL parameters + grid/solution C Put semi-discrete PDE system + Dorfi&Drury grid equation in DASSL C Write grid and solution at specific steps (TPRINT) to outputfile C C Problem choice by loading the specific problem file with the modules: C C SUBROUTINE INIPRB (TEXT) C CHARACTER TEXT*80 C Initialize /PROBLM/ C C SUBROUTINE UINIT (NPDE, NPTS, Y) C INTEGER NPDE, NPTS C REAL Y(NPDE+1,NPTS) C Initial solution; optionnally redefinition of (uniform) grid C C SUBROUTINE SPDEF (T,X,NPDE, U, DUDX, C, Q, R, IRES) C INTEGER NPDE, IRES C REAL T, X C REAL U(NPDE), DUDX(NPDE), C(NPDE,NPDE), Q(NPDE), R(NPDE) C PDE defining functions C, Q, R C C SUBROUTINE BNDR (T, BETA, GAMMA, U, UX, NPDE, LEFT, IRES) C INTEGER NPDE, IRES C LOGICAL LEFT C REAL T C REAL BETA(NPDE), GAMMA(NPDE), U(NPDE), UX(NPDE) C Boundary function C C SUBROUTINE UEXACT (X, T, U) C REAL X, T C REAL U(NPDE) C Exact solution (only called if SOLAV=TRUE) C How to use the interface in a DASSL environment: ----------------------------------------------- Compile and link the files DRIVER SPMDIF MACHAR SDASSL DASUSE DASLIP and one of the problem dependent routines PRB... NB. If PRBDSH is used the TAU parameter in DRIVER should be set to == TAU = 1E-3 since the initial grid is not consistent with the DAE system. The results and integration information can be found in the corresponding files RES... RUN... C C####################################################################### C C MIFDOC : software documentation of the moving-grid interface itself. C C####################################################################### C C----------------------------------------------------------------------- C C Moving grid discretization module SPMDIF C ---------------------------------------- C This module discretizes systems of partial differential equations C in one space variable on a moving grid. The class of equations that C can be handled is given by C C NPDE k -m m C sum C (x,t, u, u ) u + Q (x,t, u, u ) = x (x R (x,t, u, u )) C k=1 j,k - -x t j - -x j - -x x C C where 1 NPDE T C u = ( u , ... , u ) , j = 1,... , NPDE, C - C k C and u is the partial derivative wrt time of the k-th component of u. C t C C The functions C, Q, and R are assumed to be continuous w.r.t. the C space variable. C C The independent variables x and t satisfy x < x < x with x and x C L R L R C fixed and t > t . C 0 C The boundary conditions have the form C C BETA(x,t).R(x,t,u,u ) = GAMMA(x,t,u,u ) at x = x , x , C - -x - -x L R C C where not all of the functions BETA and GAMMA are set to zero. C C The initial conditions are given by C 0 C u (x,t ) = u (x) for x <= x <= x . C - 0 - L R C The discretization method for the PDE in Lagrangian formulation C used by this module is based on a lumped Galerkin / Petrov-Galerkin C method and evaluates the PDE functions in a point between C the (moving) grid points. C C References: C Fixed-grid spatial discretization C Skeel R.D. and Berzins M. C A Method for the Spatial Discretisation of Parabolic C Equations in one Space Variable. C Leeds Report no 217, C Dept. of Computer Studies, The University. C Grid movement C Verwer J.G., Blom J.G., Furzeland R.M. and Zegeling P.A. C A Moving-Grid Method for One-Dimensional PDEs based on C the Method of Lines. C Report NM-R8818, C Centre for Mathematics and Computer Science, Amsterdam. C Interface C Blom J.G. and Zegeling P.A. C A Moving-Grid Interface for Systems of One-Dimensional C Time-Dependent Partial Differential Equations. C Report NM-R8904, C Centre for Mathematics and Computer Science, Amsterdam. C (ACM TOMS algorithm) C C---------------------------------------------------------------------- C C How to use this module C ---------------------- C 1. Set NPDE = # PDEs to be solved. C Set NPTS = # mesh points to be used. C (NC=NPTS-2 is # internal points) C Set M for space coordinate type C = 0 for Cartesian, = 1 for cylindrical, = 2 for spherical. C Specify a workspace of size at least (NPDE+1)*NPTS+(6+NPDE)*NPDE C for use by the routine SKMRES which defines the DAE system being C solved by the integrator. C C Call the initialization routine SETSKM, see the documentation at C the head of this routine for the precise details of the call. C C Set TS and TOUT for start and end integration times. C Initialize data as required for time integration, C - see documentation of DAE solver. C Call the DAE solver with as residual routine SKMRES or an C enveloping routine to satisfy the header requirements. C C 2. Provide a set of routines which describe the precise form of the C PDEs to be solved. Three routines must be provided and the names C of these routines are fixed. These routines are: C SPDEF forms the functions C, Q and R of the PDE in a C given x-point. C BNDR forms the functions BETA and GAMMA associated with the C boundary conditions for the PDE. C UINIT supplies the initial values of the PDE part. C An initial uniform grid is generated by SETSKM and C provided in Y(NPDE+1,I), I=1,NPTS. If required, a user C can redefine the mesh in a nonuniform way. C The headers of these routines are: C C SUBROUTINE SPDEF (T, X, NPDE, U, DUDX, C, Q, R, IRES) C INTEGER NPDE, IRES C REAL T, X C REAL U(NPDE), DUDX(NPDE), C(NPDE,NPDE), Q(NPDE), R(NPDE) C C SUBROUTINE BNDR (T, BETA, GAMMA, U, DUDX, NPDE, LEFT, IRES) C INTEGER NPDE, IRES C LOGICAL LEFT C REAL T C REAL BETA(NPDE), GAMMA(NPDE), U(NPDE), DUDX(NPDE) C C SUBROUTINE UINIT (NPDE, NPTS, Y) C INTEGER NPDE, NPTS C REAL Y(NPDE+1,NPTS) C C C Example problem C --------------- C The easiest way to describe how the problem description routines C should be written is by a simple example. Consider the following C problem from electrodynamics C u = eps.p.u - g(u-v) C t xx C and (so m = 0 and NPDE = 2) C v = p.v + g(u-v) C t xx C with C g(z) = exp(eta.z/3) - exp(-2.eta.z/3) , C 0 <= x <= 1 and 0 <= t <= 4; C eps = 0.143, p = 0.1743, and eta = 17.19. C C The left boundary condition (LEFT = .TRUE.) is given by C u = 0 and v = 0 at x = 0, C x C the right boundary condition (LEFT = .FALSE.) is C u = 0 and v = 0 at x = 1, C x C and the initial conditions are C u = 1 and v = 0 at t = 0. C C The routines UINIT, SPDEF and BNDR are listed below. C The component u of the PDE at the i-th grid point is held as Y(1,i) C in the package, the component v as Y(2,i); the i-th grid point C itself is stored in Y(3,i). C C C C SUBROUTINE UINIT (NPDE, NPTS, Y) C C Routine for PDE initial values. C Entry: C Y(NPDE+1,i) = x_i; uniform mesh, generated by package C Exit: C Y(NPDE+1,i) = x_i; mesh, optionally changed by user C Y( k,i) = u_k(x_i,t0); initial value of k-th component C i = 1,.., NPTS C C INTEGER NPDE, NPTS C REAL Y(NPDE+1,NPTS) C C INTEGER I C C DO 10 I = 1, NPTS C Y(1,I) = 1.0 C Y(2,I) = 0.0 C 10 CONTINUE C C RETURN C END C C C C SUBROUTINE SPDEF (T, X, NPDE, U, DUDX, C, Q, R, IRES) C C Routine to describe the body of the PDE system. C The PDE is written as C NPDE k -m m C sum C (x,t,u,u ) u + Q (x,t,u,u ) = x (x R (x,t,u,u ) ) . C k=1 jk x t j x j x x C The functions C, Q and R must be defined in this routine. C C INTEGER NPDE, IRES C REAL T, X C REAL U(NPDE), DUDX(NPDE), C(NPDE,NPDE), Q(NPDE), R(NPDE) C C INTEGER J, K C REAL EPS, ETA, GZ, P, Z C DATA EPS /0.143/, ETA /17.19/, P /0.1743/ C C DO 10 K = 1, NPDE C DO 20 J = 1, NPDE C C(J,K) = 0.0 C 20 CONTINUE C C(K,K) = 1.0 C 10 CONTINUE C C Z = U(1) - U(2) C GZ = EXP(ETA*Z/3) - EXP(-2*ETA*Z/3) C Q(1) = GZ C Q(2) = -GZ C C R(1) = EPS*P * DUDX(1) C R(2) = P * DUDX(2) C C RETURN C END C C C C SUBROUTINE BNDR (T, BETA, GAMMA, U, DUDX, NPDE, LEFT, IRES) C C Boundary conditions routine C The boundary conditions are written as C BETA (x,t) R (x,t,u,u ) = GAMMA (x,t,u,u ) C j j x j x C The functions BETA and GAMMA should be defined in this routine. C C INTEGER NPDE, IRES C LOGICAL LEFT C REAL T C REAL BETA(NPDE), GAMMA(NPDE), U(NPDE), DUDX(NPDE) C C IF (LEFT) THEN C BETA (1) = 1.0 C GAMMA(1) = 0.0 C BETA (2) = 0.0 C GAMMA(2) = U(2) C ELSE C BETA (1) = 0.0 C GAMMA(1) = U(1) - 1.0 C BETA (2) = 1.0 C GAMMA(2) = 0.0 C ENDIF C C RETURN C END C C C####################################################################### C C RESBAK : RESULT file from single precision version C for the first example problem C C####################################################################### C Bakker, Electrodynamics problem; EPS=0.143, P=0.1743, ETA=17.19 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 -T= 0.00000E+00 X(S,TN): 0.00000000000000E+00 0.50000000000000E-01 0.10000000000000E+00 0.15000000000000E+00 0.20000000000000E+00 0.25000000000000E+00 0.30000000000000E+00 0.35000000000000E+00 0.40000000000000E+00 0.45000000000000E+00 0.50000000000000E+00 0.55000000000000E+00 0.60000000000000E+00 0.65000000000000E+00 0.70000000000000E+00 0.75000000000000E+00 0.80000000000000E+00 0.85000000000000E+00 0.90000000000000E+00 0.95000000000000E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 -T= 0.10000E-03 X(S,TN): -0.45929255914759E-19 0.25040640290220E-01 0.56481182704547E-01 0.95013746311533E-01 0.14035701231943E+00 0.19172997170988E+00 0.24805286040399E+00 0.30815425177574E+00 0.37092073056414E+00 0.43536105966516E+00 0.50059965537049E+00 0.56582746970413E+00 0.63023451172673E+00 0.69294260800311E+00 0.75295709500441E+00 0.80916185657288E+00 0.86038575610616E+00 0.90555452167634E+00 0.94389834759477E+00 0.97514972312581E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.97256278203386E+00 0.97297329460978E+00 0.97347359747748E+00 0.97362279769018E+00 0.97365968612859E+00 0.97366795251495E+00 0.97366993754457E+00 0.97367061718684E+00 0.97367094665945E+00 0.97367111097203E+00 0.97367116090931E+00 0.97367110995003E+00 0.97367094675137E+00 0.97367066002049E+00 0.97367048643146E+00 0.97367279232644E+00 0.97369354243553E+00 0.97382236618489E+00 0.97451336969171E+00 0.97805479165282E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 0.10158626506619E-16 0.21863836925754E-01 0.25474655206463E-01 0.26176978370070E-01 0.26306690064825E-01 0.26327294436488E-01 0.26329526698004E-01 0.26329338707842E-01 0.26329051464071E-01 0.26328889377324E-01 0.26328839457234E-01 0.26328890549432E-01 0.26329056717380E-01 0.26329390760117E-01 0.26330088342959E-01 0.26332151381840E-01 0.26340710279631E-01 0.26378419427779E-01 0.26528830856401E-01 0.27025637008333E-01 0.27429641024853E-01 Statistics: FNS, JACS:25, 9 STEPS, ETF, CTF:14, 0, 0 -T= 0.10000E-02 X(S,TN): 0.10096741302168E-15 0.12035719074328E-01 0.27659128209353E-01 0.49865220895497E-01 0.81605103543717E-01 0.12602462914175E+00 0.18619247847968E+00 0.26401810016408E+00 0.35861164907025E+00 0.46490893940724E+00 0.57403954521281E+00 0.67610235632744E+00 0.76369477884377E+00 0.83368267073946E+00 0.88661980899191E+00 0.92509600342961E+00 0.95229367331208E+00 0.97117431687522E+00 0.98419344028329E+00 0.99327637270227E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.84124639415634E+00 0.85198008579324E+00 0.86417805594088E+00 0.86767855237370E+00 0.86870605053580E+00 0.86901606826152E+00 0.86910499154684E+00 0.86912953917044E+00 0.86913887899673E+00 0.86914157341817E+00 0.86913640670443E+00 0.86912565320049E+00 0.86912013781261E+00 0.86915098186856E+00 0.86930686492989E+00 0.86979879062790E+00 0.87108032245948E+00 0.87416884320602E+00 0.88202791044688E+00 0.90698269192593E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 0.12906845854695E-14 0.85805240030432E-01 0.11962492264781E+00 0.12841936270931E+00 0.13028720055180E+00 0.13074916685063E+00 0.13085454382600E+00 0.13086676156911E+00 0.13086128635510E+00 0.13085860201449E+00 0.13086418709539E+00 0.13087854363622E+00 0.13090461500711E+00 0.13096181033273E+00 0.13110840596252E+00 0.13150473184524E+00 0.13256554012321E+00 0.13517998806772E+00 0.14028780604146E+00 0.14665928624041E+00 0.14940963004855E+00 Statistics: FNS, JACS:61, 13 STEPS, ETF, CTF:33, 0, 0 -T= 0.10000E-01 X(S,TN): 0.12321694707397E-15 0.16259046659784E-01 0.34383535895571E-01 0.56835836175499E-01 0.87041130186527E-01 0.12957612320856E+00 0.18909463247710E+00 0.26896987480346E+00 0.36926606771224E+00 0.48381928143333E+00 0.60023366312207E+00 0.70518181363670E+00 0.79064082999200E+00 0.85527719537961E+00 0.90186409643097E+00 0.93448369137719E+00 0.95706820877491E+00 0.97276825821681E+00 0.98401711038015E+00 0.99265720180072E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.55402306951480E+00 0.58108910541637E+00 0.63225213431880E+00 0.66627322477729E+00 0.68085414520969E+00 0.68521098036305E+00 0.68607431016619E+00 0.68618613358218E+00 0.68620358427590E+00 0.68620857279386E+00 0.68620575805936E+00 0.68620193948851E+00 0.68622622321513E+00 0.68640895842475E+00 0.68722049724873E+00 0.68983177811135E+00 0.69843379361656E+00 0.72636152222943E+00 0.78483376221049E+00 0.87331914958560E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 -0.14423510781113E-15 0.10434572933473E+00 0.18773200936252E+00 0.25316318733207E+00 0.29495829171579E+00 0.31083861716651E+00 0.31358221957824E+00 0.31379496379115E+00 0.31379634997062E+00 0.31379210702118E+00 0.31379639822638E+00 0.31381263466474E+00 0.31387638022552E+00 0.31432301373424E+00 0.31681082856067E+00 0.32390520899290E+00 0.33490016491657E+00 0.34648401666759E+00 0.35618494627395E+00 0.36293229887844E+00 0.36542563003615E+00 Statistics: FNS, JACS:87, 16 STEPS, ETF, CTF:50, 0, 0 -T= 0.10000E+00 X(S,TN): 0.14331098239068E-15 0.27509483466300E-01 0.55993853613377E-01 0.86797397243380E-01 0.12184131719335E+00 0.16382468916371E+00 0.21644008503414E+00 0.28414150959066E+00 0.37020737682426E+00 0.47234901909983E+00 0.58046996527423E+00 0.68113151533455E+00 0.76479022471584E+00 0.82907726170566E+00 0.87662281502272E+00 0.91151541453917E+00 0.93755459576611E+00 0.95766091089810E+00 0.97387210855655E+00 0.98760829949711E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.21974534394379E+00 0.24082376269937E+00 0.29058114641601E+00 0.34867167626356E+00 0.40416712783431E+00 0.44973781796411E+00 0.48125524138903E+00 0.49908680544002E+00 0.50698569979986E+00 0.50962245266198E+00 0.51055292014141E+00 0.51203188913654E+00 0.51609479116237E+00 0.52517648903438E+00 0.54436694256418E+00 0.58048272381257E+00 0.63431426634869E+00 0.70289964791332E+00 0.78413731636754E+00 0.87974885845813E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 -0.18368361340501E-14 0.88797802893640E-01 0.16833570592607E+00 0.24183227161984E+00 0.31039168545408E+00 0.37292535255351E+00 0.42566498790975E+00 0.46296747411637E+00 0.48196669098422E+00 0.48823941471498E+00 0.49030543486261E+00 0.49378948087089E+00 0.50305406913238E+00 0.51960809965608E+00 0.54068676663276E+00 0.56194272044633E+00 0.58032800498320E+00 0.59478225700266E+00 0.60534675177147E+00 0.61217120657784E+00 0.61461802433752E+00 Statistics: FNS, JACS:109, 18 STEPS, ETF, CTF:67, 0, 0 -T= 0.25000E+00 X(S,TN): 0.12725037865343E-15 0.35291254425231E-01 0.71018499650379E-01 0.10814727313561E+00 0.14806484107473E+00 0.19254359390664E+00 0.24383356497859E+00 0.30463589317156E+00 0.37745877336233E+00 0.46262763941150E+00 0.55547608492964E+00 0.64660341650348E+00 0.72720823654849E+00 0.79352530583887E+00 0.84616098410961E+00 0.88743116331616E+00 0.91981720922314E+00 0.94553081719465E+00 0.96644700465101E+00 0.98413122687172E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.10805691125032E+00 0.12867780638170E+00 0.17698893961420E+00 0.23411712654762E+00 0.29233041000358E+00 0.34784124009268E+00 0.39770932046008E+00 0.43884543498730E+00 0.46883295790019E+00 0.48788841142235E+00 0.50012006547364E+00 0.51181131222257E+00 0.52821187130139E+00 0.55126970203934E+00 0.58088153128989E+00 0.61789323477408E+00 0.66469191726619E+00 0.72340650173389E+00 0.79551790787835E+00 0.88411328778420E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 0.32113325487618E-14 0.74015549627789E-01 0.14091574007736E+00 0.20354615192433E+00 0.26322295556401E+00 0.32010382632822E+00 0.37315587636328E+00 0.41999805889254E+00 0.45728004537205E+00 0.48295016505953E+00 0.50002278877089E+00 0.51592872114635E+00 0.53662059145540E+00 0.56286195944614E+00 0.59169029042505E+00 0.61938021532653E+00 0.64316739171925E+00 0.66177161083460E+00 0.67509344374135E+00 0.68341946465375E+00 0.68632734130789E+00 Statistics: FNS, JACS:117, 19 STEPS, ETF, CTF:74, 0, 0 -T= 0.50000E+00 X(S,TN): 0.14309716753197E-15 0.44439184054847E-01 0.88805154702960E-01 0.13392003828239E+00 0.18087866430320E+00 0.23083518694143E+00 0.28495809726599E+00 0.34430991038575E+00 0.40951532593247E+00 0.48017618529946E+00 0.55428281061888E+00 0.62829230260064E+00 0.69829246288909E+00 0.76140048913084E+00 0.81625745109764E+00 0.86267957209169E+00 0.90118663330737E+00 0.93275317065160E+00 0.95869695796909E+00 0.98054839125876E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.61705872700837E-01 0.83571830093333E-01 0.13215150721409E+00 0.18633482340289E+00 0.24042708729016E+00 0.29267592896158E+00 0.34206223729876E+00 0.38753962103392E+00 0.42811975474081E+00 0.46346837107444E+00 0.49467327599739E+00 0.52422241421676E+00 0.55451688142558E+00 0.58639607641640E+00 0.61954782368977E+00 0.65442523020765E+00 0.69380864711304E+00 0.74236191663913E+00 0.80489381307507E+00 0.88669439366782E+00 0.99999999999999E+00 U(X(S,TN),TN), COMP:2 0.29357275824825E-14 0.63742469167286E-01 0.12163927031717E+00 0.17672723402117E+00 0.22997910286532E+00 0.28151552181222E+00 0.33094496061509E+00 0.37748421738985E+00 0.42020712674656E+00 0.45860618995472E+00 0.49330124460705E+00 0.52612422735900E+00 0.55894416347117E+00 0.59231651008286E+00 0.62533800603176E+00 0.65630895899070E+00 0.68338628129423E+00 0.70513609405918E+00 0.72093103881909E+00 0.73076722895464E+00 0.73416672114764E+00 Statistics: FNS, JACS:125, 20 STEPS, ETF, CTF:80, 0, 0 -T= 0.10000E+01 X(S,TN): 0.15579464091624E-15 0.54377796631882E-01 0.10808499702755E+00 0.16166534113479E+00 0.21573577426543E+00 0.27077941894134E+00 0.32712512028561E+00 0.38491631485438E+00 0.44407755115856E+00 0.50430143165554E+00 0.56502076662724E+00 0.62539846087767E+00 0.68439978007837E+00 0.74088134783070E+00 0.79366740937016E+00 0.84166569394911E+00 0.88403012922474E+00 0.92037830480956E+00 0.95100855908446E+00 0.97697228843874E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.41855939535181E-01 0.64374251707875E-01 0.11186576987393E+00 0.16204980866788E+00 0.21164682386363E+00 0.26020607448425E+00 0.30762778791832E+00 0.35384089867530E+00 0.39881014785837E+00 0.44257057790027E+00 0.48519340782749E+00 0.52670743080367E+00 0.56703180609075E+00 0.60593798951026E+00 0.64314500553159E+00 0.67890444579687E+00 0.71527246918554E+00 0.75721065734866E+00 0.81192653120524E+00 0.88782968033196E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 -0.29428837436846E-14 0.57131864288686E-01 0.10922404384575E+00 0.15955951890530E+00 0.20880629258781E+00 0.25712185005723E+00 0.30452055106568E+00 0.35095994941793E+00 0.39640073540404E+00 0.44081243225129E+00 0.48416051562390E+00 0.52638421227051E+00 0.56733409386149E+00 0.60668419317797E+00 0.64387198669139E+00 0.67806789646732E+00 0.70817472279515E+00 0.73294873042647E+00 0.75138144575774E+00 0.76298926846214E+00 0.76699655461490E+00 Statistics: FNS, JACS:134, 22 STEPS, ETF, CTF:87, 0, 0 -T= 0.20000E+01 X(S,TN): 0.29409680181596E-15 0.60053312578581E-01 0.11903677672934E+00 0.17727611123687E+00 0.23511706509967E+00 0.29279165598505E+00 0.35043595339502E+00 0.40810238795770E+00 0.46575791994838E+00 0.52327779388177E+00 0.58042955175588E+00 0.63684463711884E+00 0.69199400983232E+00 0.74516472209928E+00 0.79546441287016E+00 0.84188932882871E+00 0.88349316596151E+00 0.91966692030223E+00 0.95044811298548E+00 0.97668380211812E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.35153306610654E-01 0.57866835981245E-01 0.10462817309598E+00 0.15300641642817E+00 0.20100810899407E+00 0.24855287024443E+00 0.29567823589677E+00 0.34238440863736E+00 0.38862216690770E+00 0.43429254093055E+00 0.47923385334969E+00 0.52319895985026E+00 0.56583652449281E+00 0.60670223125468E+00 0.64540338585039E+00 0.68213406960155E+00 0.71883586428744E+00 0.76036192060918E+00 0.81407465320883E+00 0.88880160013576E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 0.83672220273541E-14 0.54320856370252E-01 0.10405126664540E+00 0.15262122839213E+00 0.20056433684308E+00 0.24804132895257E+00 0.29511679638358E+00 0.34179518052582E+00 0.38802979007883E+00 0.43372020420521E+00 0.47869659580729E+00 0.52270542162762E+00 0.56538312543830E+00 0.60622865018382E+00 0.64459146390332E+00 0.67964650343230E+00 0.71036886968219E+00 0.73560345360282E+00 0.75438217175095E+00 0.76620774946117E+00 0.77028755821621E+00 Statistics: FNS, JACS:141, 23 STEPS, ETF, CTF:92, 0, 0 -T= 0.30000E+01 X(S,TN): 0.28573248148445E-15 0.61545078541541E-01 0.12195028465348E+00 0.18152001114298E+00 0.24056090084449E+00 0.29926758441615E+00 0.35774357225620E+00 0.41601581266998E+00 0.47403676436145E+00 0.53167582403960E+00 0.58870138247998E+00 0.64475520163642E+00 0.69932378731912E+00 0.75171728897627E+00 0.80107736495090E+00 0.84644881821691E+00 0.88695344395276E+00 0.92206692122934E+00 0.95190595527069E+00 0.97735239318904E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.33958724409891E-01 0.56829997983521E-01 0.10362924441254E+00 0.15176444318814E+00 0.19952056487269E+00 0.24686675541916E+00 0.29384675605411E+00 0.34046027313350E+00 0.38665455929641E+00 0.43231818382776E+00 0.47726846727143E+00 0.52123386881998E+00 0.56383965630444E+00 0.60463095475969E+00 0.64324849097419E+00 0.68001327241054E+00 0.71707805635342E+00 0.75938810677969E+00 0.81403088298383E+00 0.88929997660461E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 -0.19060764564055E-14 0.53908575476223E-01 0.10328102875282E+00 0.15158885010453E+00 0.19932380863160E+00 0.24663694326002E+00 0.29358882170883E+00 0.34018116733100E+00 0.38636162646034E+00 0.43201868525592E+00 0.47696902789347E+00 0.52093896719268E+00 0.56354233961505E+00 0.60425935917571E+00 0.64241850304921E+00 0.67717428866561E+00 0.70749185143344E+00 0.73224719410853E+00 0.75056556132342E+00 0.76205903957098E+00 0.76602026680388E+00 Statistics: FNS, JACS:146, 24 STEPS, ETF, CTF:95, 0, 0 -T= 0.40000E+01 X(S,TN): -0.85468233905893E-16 0.62278089651929E-01 0.12338589600318E+00 0.18362097106100E+00 0.24327343518029E+00 0.30252134231709E+00 0.36145307371032E+00 0.42008210677703E+00 0.47834931144713E+00 0.53611463939805E+00 0.59313955698469E+00 0.64906209169345E+00 0.70336918356199E+00 0.75537733328420E+00 0.80424320252131E+00 0.84903886446402E+00 0.88892831962760E+00 0.92344078672753E+00 0.95274240063757E+00 0.97773675557374E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.33421631420763E-01 0.56380094159363E-01 0.10321815438402E+00 0.15125338833211E+00 0.19890283667247E+00 0.24615552130313E+00 0.29305621644875E+00 0.33960294650938E+00 0.38574020556715E+00 0.43135247048215E+00 0.47625139131189E+00 0.52015834994579E+00 0.56269167606630E+00 0.60339604193638E+00 0.64193674077807E+00 0.67871347153285E+00 0.71600107567396E+00 0.75878543377197E+00 0.81398050494738E+00 0.88957192118291E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:2 -0.57131982845478E-15 0.53737185559809E-01 0.10295746219314E+00 0.15115351828478E+00 0.19879595065330E+00 0.24603024097559E+00 0.29291446209511E+00 0.33944809845995E+00 0.38557597776079E+00 0.43118267915336E+00 0.47607961326666E+00 0.51998620953497E+00 0.56250800482608E+00 0.60311585136995E+00 0.64112759825094E+00 0.67568618264273E+00 0.70575090826504E+00 0.73021685319163E+00 0.74826369867698E+00 0.75956434986654E+00 0.76345718816966E+00 Statistics: FNS, JACS:147, 24 STEPS, ETF, CTF:96, 0, 0 C C####################################################################### C C RUNBAK : RUNINF file from single precision version C for the first example problem C C####################################################################### C Bakker, Electrodynamics problem; EPS=0.143, P=0.1743, ETA=17.19 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 Time= 0.20000E-06; H= 0.10000E-06; Order= 1 Time= 0.40000E-06; H= 0.20000E-06; Order= 2 Time= 0.80000E-06; H= 0.40000E-06; Order= 1 Time= 0.16000E-05; H= 0.80000E-06; Order= 1 Time= 0.32000E-05; H= 0.16000E-05; Order= 1 Time= 0.64000E-05; H= 0.32000E-05; Order= 1 Time= 0.12800E-04; H= 0.64000E-05; Order= 1 Time= 0.19200E-04; H= 0.64000E-05; Order= 1 Time= 0.25600E-04; H= 0.64000E-05; Order= 1 Time= 0.38400E-04; H= 0.12800E-04; Order= 2 Time= 0.51200E-04; H= 0.12800E-04; Order= 2 Time= 0.64000E-04; H= 0.12800E-04; Order= 2 Time= 0.76800E-04; H= 0.12800E-04; Order= 2 Time= 0.10240E-03; H= 0.25600E-04; Order= 2 Time= 0.12800E-03; H= 0.25600E-04; Order= 1 Time= 0.15104E-03; H= 0.23040E-04; Order= 1 Time= 0.17408E-03; H= 0.23040E-04; Order= 1 Time= 0.19712E-03; H= 0.23040E-04; Order= 1 Time= 0.24320E-03; H= 0.46080E-04; Order= 2 Time= 0.28928E-03; H= 0.46080E-04; Order= 2 Time= 0.33536E-03; H= 0.46080E-04; Order= 2 Time= 0.38144E-03; H= 0.46080E-04; Order= 2 Time= 0.42752E-03; H= 0.46080E-04; Order= 2 Time= 0.47360E-03; H= 0.46080E-04; Order= 3 Time= 0.51968E-03; H= 0.46080E-04; Order= 2 Time= 0.56576E-03; H= 0.46080E-04; Order= 2 Time= 0.61184E-03; H= 0.46080E-04; Order= 2 Time= 0.65792E-03; H= 0.46080E-04; Order= 2 Time= 0.70400E-03; H= 0.46080E-04; Order= 1 Time= 0.75008E-03; H= 0.46080E-04; Order= 1 Time= 0.84224E-03; H= 0.92160E-04; Order= 1 Time= 0.93440E-03; H= 0.92160E-04; Order= 1 Time= 0.10266E-02; H= 0.92160E-04; Order= 1 Time= 0.12109E-02; H= 0.18432E-03; Order= 2 Time= 0.13952E-02; H= 0.18432E-03; Order= 2 Time= 0.17638E-02; H= 0.36864E-03; Order= 2 Time= 0.20956E-02; H= 0.33178E-03; Order= 2 Time= 0.24274E-02; H= 0.33178E-03; Order= 2 Time= 0.27592E-02; H= 0.33178E-03; Order= 2 Time= 0.30909E-02; H= 0.33178E-03; Order= 2 Time= 0.34227E-02; H= 0.33178E-03; Order= 3 Time= 0.40863E-02; H= 0.66355E-03; Order= 3 Time= 0.47498E-02; H= 0.66355E-03; Order= 3 Time= 0.54134E-02; H= 0.66355E-03; Order= 3 Time= 0.60769E-02; H= 0.66355E-03; Order= 3 Time= 0.67405E-02; H= 0.66355E-03; Order= 2 Time= 0.74040E-02; H= 0.66355E-03; Order= 2 Time= 0.80676E-02; H= 0.66355E-03; Order= 2 Time= 0.87311E-02; H= 0.66355E-03; Order= 2 Time= 0.10058E-01; H= 0.13271E-02; Order= 2 Time= 0.11385E-01; H= 0.13271E-02; Order= 2 Time= 0.12712E-01; H= 0.13271E-02; Order= 2 Time= 0.15367E-01; H= 0.26542E-02; Order= 2 Time= 0.18021E-01; H= 0.26542E-02; Order= 2 Time= 0.20675E-01; H= 0.26542E-02; Order= 2 Time= 0.23329E-01; H= 0.26542E-02; Order= 2 Time= 0.28638E-01; H= 0.53084E-02; Order= 3 Time= 0.33946E-01; H= 0.53084E-02; Order= 3 Time= 0.39255E-01; H= 0.53084E-02; Order= 3 Time= 0.44563E-01; H= 0.53084E-02; Order= 3 Time= 0.49871E-01; H= 0.53084E-02; Order= 3 Time= 0.60488E-01; H= 0.10617E-01; Order= 2 Time= 0.70043E-01; H= 0.95551E-02; Order= 2 Time= 0.79598E-01; H= 0.95551E-02; Order= 2 Time= 0.89154E-01; H= 0.95551E-02; Order= 2 Time= 0.98709E-01; H= 0.95551E-02; Order= 2 Time= 0.11782E+00; H= 0.19110E-01; Order= 3 Time= 0.13693E+00; H= 0.19110E-01; Order= 3 Time= 0.15604E+00; H= 0.19110E-01; Order= 3 Time= 0.17515E+00; H= 0.19110E-01; Order= 3 Time= 0.19426E+00; H= 0.19110E-01; Order= 3 Time= 0.21337E+00; H= 0.19110E-01; Order= 2 Time= 0.23248E+00; H= 0.19110E-01; Order= 2 Time= 0.25159E+00; H= 0.19110E-01; Order= 2 Time= 0.27070E+00; H= 0.19110E-01; Order= 2 Time= 0.30892E+00; H= 0.38221E-01; Order= 2 Time= 0.34714E+00; H= 0.38221E-01; Order= 2 Time= 0.38536E+00; H= 0.38221E-01; Order= 2 Time= 0.42358E+00; H= 0.38221E-01; Order= 2 Time= 0.50003E+00; H= 0.76441E-01; Order= 3 Time= 0.57647E+00; H= 0.76441E-01; Order= 3 Time= 0.65291E+00; H= 0.76441E-01; Order= 3 Time= 0.72935E+00; H= 0.76441E-01; Order= 3 Time= 0.80579E+00; H= 0.76441E-01; Order= 2 Time= 0.88223E+00; H= 0.76441E-01; Order= 2 Time= 0.95867E+00; H= 0.76441E-01; Order= 2 Time= 0.11116E+01; H= 0.15288E+00; Order= 2 Time= 0.12644E+01; H= 0.15288E+00; Order= 2 Time= 0.14173E+01; H= 0.15288E+00; Order= 2 Time= 0.15702E+01; H= 0.15288E+00; Order= 2 Time= 0.18760E+01; H= 0.30576E+00; Order= 3 Time= 0.21817E+01; H= 0.30576E+00; Order= 2 Time= 0.24875E+01; H= 0.30576E+00; Order= 1 Time= 0.27933E+01; H= 0.30576E+00; Order= 1 Time= 0.34048E+01; H= 0.61153E+00; Order= 1 C C####################################################################### C C RESCYL : RESULT file from single precision version C for the second example problem C C####################################################################### C Reaction-diffusion prob. in cyl. coord.; pars: 1.00000 0.00010 1.00000 0.10000 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 -T= 0.00000E+00 X(S,TN): 0.00000000000000E+00 0.50000000000000E-01 0.10000000000000E+00 0.15000000000000E+00 0.20000000000000E+00 0.25000000000000E+00 0.30000000000000E+00 0.35000000000000E+00 0.40000000000000E+00 0.45000000000000E+00 0.50000000000000E+00 0.55000000000000E+00 0.60000000000000E+00 0.65000000000000E+00 0.70000000000000E+00 0.75000000000000E+00 0.80000000000000E+00 0.85000000000000E+00 0.90000000000000E+00 0.95000000000000E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 -T= 0.10000E+00 X(S,TN): 0.17639148112380E-13 0.14518591720821E+00 0.28623494020569E+00 0.41908322853390E+00 0.53995112401876E+00 0.64574669552204E+00 0.73456039093228E+00 0.80600852725463E+00 0.86120333572151E+00 0.90233799155354E+00 0.93209672542039E+00 0.95314513173228E+00 0.96780024888720E+00 0.97792439515230E+00 0.98491408768422E+00 0.98976154174569E+00 0.99315738692336E+00 0.99558121156001E+00 0.99737371803429E+00 0.99878320185078E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.10541348790610E+00 0.10543381958359E+00 0.10542847038094E+00 0.10542698561245E+00 0.10541941978923E+00 0.10539932404643E+00 0.10534688430917E+00 0.10522617224345E+00 0.10497842123410E+00 0.10451684160996E+00 0.10371988734721E+00 0.10243217794020E+00 0.10051941919686E+00 0.97874678559643E-01 0.94308534012330E-01 0.89498381115413E-01 0.82617079787539E-01 0.71960844347622E-01 0.55520642130282E-01 0.32050097751653E-01 0.00000000000000E+00 Statistics: FNS, JACS:71, 14 STEPS, ETF, CTF:34, 1, 0 -T= 0.20000E+00 X(S,TN): 0.20148591518961E-13 0.18674340180469E+00 0.36161731116823E+00 0.51532438837841E+00 0.64273542221454E+00 0.74303051546301E+00 0.81863893632480E+00 0.87370917883180E+00 0.91278857212731E+00 0.94000368973643E+00 0.95871221473832E+00 0.97147405730986E+00 0.98015664892324E+00 0.98607530283489E+00 0.99014066752644E+00 0.99298520768168E+00 0.99504836858055E+00 0.99662402836551E+00 0.99789913025558E+00 0.99899465059233E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.22303662617181E+00 0.22309304027603E+00 0.22307433305738E+00 0.22305843255700E+00 0.22301924865414E+00 0.22293473648429E+00 0.22275310329416E+00 0.22239755183779E+00 0.22175950703551E+00 0.22069641796987E+00 0.21903533515918E+00 0.21658489570770E+00 0.21305474068454E+00 0.20760619886524E+00 0.19806933569841E+00 0.18136162840480E+00 0.15640109612775E+00 0.12479284080450E+00 0.88216927894771E-01 0.47050672011424E-01 0.00000000000000E+00 Statistics: FNS, JACS:80, 15 STEPS, ETF, CTF:40, 1, 0 -T= 0.30000E+00 X(S,TN): 0.53661140544489E-13 0.20596987672642E+00 0.39457337922663E+00 0.55404366042406E+00 0.68026638445410E+00 0.77520770909444E+00 0.84399862769418E+00 0.89253997394126E+00 0.92617272732337E+00 0.94919191822873E+00 0.96482593746435E+00 0.97540703067471E+00 0.98257233151908E+00 0.98745437274742E+00 0.99084192915820E+00 0.99328247630039E+00 0.99513367305359E+00 0.99661547342145E+00 0.99786366560713E+00 0.99896844131509E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.35555856393790E+00 0.35564179498772E+00 0.35561290333202E+00 0.35558216590891E+00 0.35551283442850E+00 0.35537111488340E+00 0.35508524839620E+00 0.35455436764313E+00 0.35364048125503E+00 0.35216510754008E+00 0.34989533767351E+00 0.34641973140339E+00 0.34044163235663E+00 0.32826224149205E+00 0.30487105733613E+00 0.26953320481898E+00 0.22564359591173E+00 0.17619233914351E+00 0.12247986317158E+00 0.64325923644970E-01 0.00000000000000E+00 Statistics: FNS, JACS:88, 16 STEPS, ETF, CTF:43, 1, 0 -T= 0.40000E+00 X(S,TN): 0.46828264956288E-13 0.21713138426698E+00 0.41308519312985E+00 0.57485266622599E+00 0.69952364253330E+00 0.79102371564955E+00 0.85599655379241E+00 0.90113656859135E+00 0.93205310200147E+00 0.95303866124057E+00 0.96721478928629E+00 0.97677836965145E+00 0.98324993850289E+00 0.98768568982783E+00 0.99082228899445E+00 0.99314935067457E+00 0.99496964590112E+00 0.99646616424957E+00 0.99775359126552E+00 0.99891044855880E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.50696401125843E+00 0.50710652721560E+00 0.50705877632246E+00 0.50699933199617E+00 0.50688770090103E+00 0.50667977952298E+00 0.50628448935737E+00 0.50557685210792E+00 0.50439029727777E+00 0.50250323286334E+00 0.49954347494264E+00 0.49438836707380E+00 0.48309753422479E+00 0.45826240765102E+00 0.41653890291630E+00 0.36194743277390E+00 0.29941381028357E+00 0.23177460801213E+00 0.15995654915335E+00 0.83410646792825E-01 0.00000000000000E+00 Statistics: FNS, JACS:92, 16 STEPS, ETF, CTF:46, 1, 0 -T= 0.50000E+00 X(S,TN): 0.40235442704946E-13 0.22455567004220E+00 0.42509797066697E+00 0.58791547997105E+00 0.71119366706334E+00 0.80028631885819E+00 0.86279267828944E+00 0.90583768172143E+00 0.93513171670697E+00 0.95492538616216E+00 0.96825745122155E+00 0.97723861568980E+00 0.98332548194889E+00 0.98753804036679E+00 0.99057496690401E+00 0.99288156839457E+00 0.99472620632395E+00 0.99627079519095E+00 0.99761843803344E+00 0.99884154065797E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.68251799340384E+00 0.68285017206474E+00 0.68275190528803E+00 0.68261318517223E+00 0.68240496603779E+00 0.68207759388020E+00 0.68151970244396E+00 0.68057848929921E+00 0.67905606584379E+00 0.67666875194884E+00 0.67273603469895E+00 0.66454508603979E+00 0.64400721976741E+00 0.60204511243175E+00 0.53992249003457E+00 0.46476299302818E+00 0.38198113027309E+00 0.29423570618217E+00 0.20218521673193E+00 0.10496198255497E+00 0.00000000000000E+00 Statistics: FNS, JACS:97, 17 STEPS, ETF, CTF:48, 1, 0 -T= 0.60000E+00 X(S,TN): 0.34921448494076E-13 0.22981439531097E+00 0.43346055130872E+00 0.59680570662002E+00 0.71893789946941E+00 0.80625675496545E+00 0.86701301185096E+00 0.90860671815138E+00 0.93680826662235E+00 0.95582461227373E+00 0.96861832147465E+00 0.97723715723382E+00 0.98309967448576E+00 0.98720152062877E+00 0.99021283166830E+00 0.99254432472928E+00 0.99444027065991E+00 0.99604950748049E+00 0.99746839647591E+00 0.99876586731933E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.88960252996354E+00 0.88999280132192E+00 0.88987395954277E+00 0.88968476961142E+00 0.88940790618994E+00 0.88898096654283E+00 0.88826891352185E+00 0.88708760048559E+00 0.88519170173226E+00 0.88216156906403E+00 0.87661606889136E+00 0.86287741230203E+00 0.82815828170659E+00 0.76514531515533E+00 0.68019050045773E+00 0.58211293088298E+00 0.47650032477986E+00 0.36587357891849E+00 0.25067036034383E+00 0.12971934592329E+00 0.00000000000000E+00 Statistics: FNS, JACS:99, 17 STEPS, ETF, CTF:50, 1, 0 -T= 0.70000E+00 X(S,TN): 0.39581058538728E-13 0.23377905361721E+00 0.43967186810861E+00 0.60328029580792E+00 0.72445454104991E+00 0.81040079391770E+00 0.86983970276644E+00 0.91035607986792E+00 0.93774942912838E+00 0.95618759355780E+00 0.96858195358542E+00 0.97693769342118E+00 0.98265523524132E+00 0.98671713234524E+00 0.98975044632721E+00 0.99213740355916E+00 0.99410577335986E+00 0.99579544804295E+00 0.99729814093372E+00 0.99868058138925E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.11405410367218E+01 0.11409879181167E+01 0.11408486427610E+01 0.11405938278885E+01 0.11402253729408E+01 0.11396651889401E+01 0.11387476237349E+01 0.11372454294993E+01 0.11348389554149E+01 0.11308433409514E+01 0.11225206803137E+01 0.10998127682288E+01 0.10462626728674E+01 0.95835064038583E+00 0.84668338522179E+00 0.72153621317234E+00 0.58878963322130E+00 0.45092145719213E+00 0.30818413233869E+00 0.15907043748619E+00 0.00000000000000E+00 Statistics: FNS, JACS:102, 17 STEPS, ETF, CTF:53, 1, 0 -T= 0.80000E+00 X(S,TN): 0.37954569523527E-13 0.23687844733439E+00 0.44446898274482E+00 0.60820018939986E+00 0.72856993752118E+00 0.81342756023689E+00 0.87184797249918E+00 0.91154257347161E+00 0.93832208815600E+00 0.95632472656709E+00 0.96842106795060E+00 0.97659284180957E+00 0.98222153825977E+00 0.98625636877570E+00 0.98931197841330E+00 0.99174981122935E+00 0.99378501575304E+00 0.99555008203255E+00 0.99713268566197E+00 0.99859734992527E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.14552451152882E+01 0.14557792622974E+01 0.14556099550085E+01 0.14552524126281E+01 0.14547403822998E+01 0.14539769354975E+01 0.14527543759338E+01 0.14507815423442E+01 0.14476047573307E+01 0.14420032892952E+01 0.14287290500702E+01 0.13914372555694E+01 0.13111127078253E+01 0.11907322842023E+01 0.10453858234411E+01 0.88684252484787E+00 0.72121918233434E+00 0.55080997935232E+00 0.37550634732565E+00 0.19331669648157E+00 0.00000000000000E+00 Statistics: FNS, JACS:107, 17 STEPS, ETF, CTF:55, 1, 0 -T= 0.90000E+00 X(S,TN): 0.47004986274091E-13 0.23938161877579E+00 0.44826364294621E+00 0.61195878884688E+00 0.73154602184655E+00 0.81542300544926E+00 0.87295424776024E+00 0.91194368711058E+00 0.93820195338006E+00 0.95583979314809E+00 0.96769734821645E+00 0.97572783224168E+00 0.98132261250638E+00 0.98543524699746E+00 0.98860502588807E+00 0.99116537947456E+00 0.99332334416035E+00 0.99520850016990E+00 0.99690765758174E+00 0.99848576494487E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.18699204923934E+01 0.18704670015640E+01 0.18702963036556E+01 0.18698193959790E+01 0.18691087247082E+01 0.18680405971782E+01 0.18663435879801E+01 0.18636221340725E+01 0.18591754243072E+01 0.18507388165997E+01 0.18289784636922E+01 0.17703324307399E+01 0.16558224901983E+01 0.14935810549739E+01 0.13037290227298E+01 0.11008273301685E+01 0.89171884784704E+00 0.67870517463195E+00 0.46132327789948E+00 0.23687936558172E+00 0.00000000000000E+00 Statistics: FNS, JACS:115, 18 STEPS, ETF, CTF:57, 1, 0 -T= 0.10000E+01 X(S,TN): 0.45801647286645E-13 0.24147668399788E+00 0.45139715052561E+00 0.61499570378881E+00 0.73386821331645E+00 0.81688088048752E+00 0.87363738806035E+00 0.91201890854393E+00 0.93783685860958E+00 0.95517539904788E+00 0.96684642682713E+00 0.97479298625964E+00 0.98038079875103E+00 0.98452195512474E+00 0.98776520396021E+00 0.99043419357391E+00 0.99272230921026E+00 0.99475033009665E+00 0.99659953020852E+00 0.99833113953327E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.24595012097713E+01 0.24600911156977E+01 0.24598879793067E+01 0.24591931750024E+01 0.24581205619298E+01 0.24564996299339E+01 0.24539415830210E+01 0.24498486518006E+01 0.24430018339040E+01 0.24290830349629E+01 0.23920605128629E+01 0.22990009497997E+01 0.21327889917527E+01 0.19119343062940E+01 0.16620837886650E+01 0.13994675928117E+01 0.11313861319206E+01 0.85984062228872E+00 0.58369866513344E+00 0.29933711963228E+00 0.00000000000000E+00 Statistics: FNS, JACS:123, 18 STEPS, ETF, CTF:60, 1, 0 C C####################################################################### C C RUNCYL : RUNINF file from single precision version C for the second example problem C C####################################################################### C Reaction-diffusion prob. in cyl. coord.; pars: 1.00000 0.00010 1.00000 0.10000 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 Time= 0.20000E-03; H= 0.10000E-03; Order= 1 Time= 0.40000E-03; H= 0.20000E-03; Order= 2 Time= 0.80000E-03; H= 0.40000E-03; Order= 1 Time= 0.16000E-02; H= 0.80000E-03; Order= 1 Time= 0.32000E-02; H= 0.16000E-02; Order= 1 Time= 0.48000E-02; H= 0.16000E-02; Order= 1 Time= 0.64000E-02; H= 0.16000E-02; Order= 1 Time= 0.96000E-02; H= 0.32000E-02; Order= 2 Time= 0.12480E-01; H= 0.28800E-02; Order= 2 Time= 0.15360E-01; H= 0.28800E-02; Order= 2 Time= 0.18240E-01; H= 0.28800E-02; Order= 2 Time= 0.21120E-01; H= 0.28800E-02; Order= 2 Time= 0.24000E-01; H= 0.28800E-02; Order= 1 Time= 0.26410E-01; H= 0.24103E-02; Order= 1 Time= 0.28821E-01; H= 0.24103E-02; Order= 1 Time= 0.31231E-01; H= 0.24103E-02; Order= 1 Time= 0.33641E-01; H= 0.24103E-02; Order= 1 Time= 0.35810E-01; H= 0.21693E-02; Order= 1 Time= 0.37586E-01; H= 0.17755E-02; Order= 1 Time= 0.39361E-01; H= 0.17755E-02; Order= 1 Time= 0.41137E-01; H= 0.17755E-02; Order= 1 Time= 0.44688E-01; H= 0.35509E-02; Order= 1 Time= 0.48239E-01; H= 0.35509E-02; Order= 1 Time= 0.51790E-01; H= 0.35509E-02; Order= 1 Time= 0.55341E-01; H= 0.35509E-02; Order= 2 Time= 0.58892E-01; H= 0.35509E-02; Order= 2 Time= 0.65993E-01; H= 0.71019E-02; Order= 2 Time= 0.73095E-01; H= 0.71019E-02; Order= 2 Time= 0.80197E-01; H= 0.71019E-02; Order= 2 Time= 0.87299E-01; H= 0.71019E-02; Order= 2 Time= 0.91368E-01; H= 0.40692E-02; Order= 1 Time= 0.95031E-01; H= 0.36623E-02; Order= 1 Time= 0.98693E-01; H= 0.36623E-02; Order= 1 Time= 0.10602E+00; H= 0.73246E-02; Order= 1 Time= 0.11334E+00; H= 0.73246E-02; Order= 1 Time= 0.12067E+00; H= 0.73246E-02; Order= 1 Time= 0.13532E+00; H= 0.14649E-01; Order= 2 Time= 0.14997E+00; H= 0.14649E-01; Order= 2 Time= 0.17926E+00; H= 0.29299E-01; Order= 2 Time= 0.20363E+00; H= 0.24371E-01; Order= 2 Time= 0.22801E+00; H= 0.24371E-01; Order= 2 Time= 0.25238E+00; H= 0.24371E-01; Order= 2 Time= 0.30112E+00; H= 0.48741E-01; Order= 2 Time= 0.34498E+00; H= 0.43867E-01; Order= 2 Time= 0.38885E+00; H= 0.43867E-01; Order= 2 Time= 0.43272E+00; H= 0.43867E-01; Order= 2 Time= 0.47659E+00; H= 0.43867E-01; Order= 2 Time= 0.52045E+00; H= 0.43867E-01; Order= 3 Time= 0.56432E+00; H= 0.43867E-01; Order= 3 Time= 0.60819E+00; H= 0.43867E-01; Order= 3 Time= 0.65205E+00; H= 0.43867E-01; Order= 3 Time= 0.69592E+00; H= 0.43867E-01; Order= 3 Time= 0.73979E+00; H= 0.43867E-01; Order= 3 Time= 0.78365E+00; H= 0.43867E-01; Order= 4 Time= 0.82752E+00; H= 0.43867E-01; Order= 4 Time= 0.87139E+00; H= 0.43867E-01; Order= 3 Time= 0.91526E+00; H= 0.43867E-01; Order= 3 Time= 0.95912E+00; H= 0.43867E-01; Order= 3 Time= 0.99734E+00; H= 0.38219E-01; Order= 3 C C####################################################################### C C RESDSH : RESULT file from single precision version !!! TAU = 1E-3 !!! C for the third example problem !!! in driver !!! C C####################################################################### C Burgers, double wave, eps=0.00100 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.100E-02, KAPPA=.200E+01, ALPHA=.100E-01 -T= 0.00000E+00 X(S,TN): 0.00000000000000E+00 0.50000000000000E-01 0.10000000000000E+00 0.15000000000000E+00 0.20000000000000E+00 0.25000000000000E+00 0.30000000000000E+00 0.35000000000000E+00 0.40000000000000E+00 0.45000000000000E+00 0.50000000000000E+00 0.55000000000000E+00 0.60000000000000E+00 0.65000000000000E+00 0.70000000000000E+00 0.75000000000000E+00 0.80000000000000E+00 0.85000000000000E+00 0.90000000000000E+00 0.95000000000000E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.99999999999306E+00 0.99999813668036E+00 0.75000000000000E+00 0.50000186331964E+00 0.50000000000691E+00 0.49999999917554E+00 0.49998184085253E+00 0.30000000000008E+00 0.10001815914748E+00 0.10000000082447E+00 0.10000000000003E+00 0.10000000000001E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 ERR_U: 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 MAX. NORM:0. TWO NORM:0. -T= 0.25000E+00 X(S,TN): -0.37891601176756E-15 0.10848055509164E+00 0.20332174224602E+00 0.27818788926894E+00 0.33366992698232E+00 0.37291449236776E+00 0.40083269943473E+00 0.42007773647351E+00 0.43538172016705E+00 0.45161440303086E+00 0.47211390316070E+00 0.49609018968139E+00 0.52169029066663E+00 0.54552369889280E+00 0.56985721764227E+00 0.60028585176896E+00 0.64240073633294E+00 0.70136740651490E+00 0.78157681490121E+00 0.88350477445082E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.10000000000000E+01 0.99716090200240E+00 0.10053914380846E+01 0.99398224508314E+00 0.99342161276444E+00 0.10192371570112E+01 0.10241375073556E+01 0.91800355662522E+00 0.70721621975003E+00 0.55195732913796E+00 0.52757264468458E+00 0.55692444902700E+00 0.54507000553550E+00 0.41902703094050E+00 0.24891573805615E+00 0.15397698065475E+00 0.12084620954434E+00 0.10668399852427E+00 0.10148885109538E+00 0.10021053851896E+00 0.10000000000000E+00 ERR_U: 0.00000000000000E+00 -0.28390979976081E-02 0.53914380846081E-02 -0.60177549168685E-02 -0.65783872328993E-02 0.19237205616918E-01 0.24189725696601E-01 -0.75660183208942E-01 -0.10747518323472E+00 0.37702670997412E-01 0.27485400773003E-01 0.56924287427126E-01 0.45079372751633E-01 -0.79875007156359E-01 -0.14573863875942E+00 0.51447659838765E-01 0.20845650165781E-01 0.66839985200429E-02 0.14888510953797E-02 0.21053851895525E-03 -0.57731597280508E-14 MAX. NORM:0.1457386387594 TWO NORM:3.6673013640631E-2 Statistics: FNS, JACS:122, 25 STEPS, ETF, CTF:54, 2, 0 -T= 0.55000E+00 X(S,TN): -0.27790329873557E-15 0.16055128031105E+00 0.30094085435990E+00 0.41131262906257E+00 0.49221934507321E+00 0.54917312062871E+00 0.58840106248221E+00 0.61518844446592E+00 0.63348452026696E+00 0.64623977482739E+00 0.65504882834307E+00 0.66207961766384E+00 0.66932004779528E+00 0.67862290146947E+00 0.69196938700943E+00 0.71174600462994E+00 0.74073205670176E+00 0.78232068363145E+00 0.83987666567841E+00 0.91417604522829E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.10000000000000E+01 0.99404747348641E+00 0.99946722007484E+00 0.10044685471444E+01 0.99915580428724E+00 0.99347717408065E+00 0.98419486010519E+00 0.99821262941603E+00 0.10343658159498E+01 0.10197795330447E+01 0.85462754390147E+00 0.55618180739419E+00 0.28636978345933E+00 0.14920826026947E+00 0.10792619259334E+00 0.10886929643692E+00 0.10812607952673E+00 0.10260598194636E+00 0.10090699464095E+00 0.10023516467595E+00 0.10000000000000E+00 ERR_U: 0.00000000000000E+00 -0.59525265135889E-02 -0.53277992516598E-03 0.44685471444339E-02 -0.84419571276584E-03 -0.65228259191130E-02 -0.15805135388920E-01 -0.17837212230880E-02 0.34720445840037E-01 0.28568673809389E-01 -0.63165151554877E-01 -0.68370543165546E-01 0.27808787742817E-01 0.23637133557707E-01 0.61141218951626E-02 0.88344851387885E-02 0.81259738311004E-02 0.26059819205542E-02 0.90699464095145E-03 0.23516467594931E-03 0.00000000000000E+00 MAX. NORM:6.8370543165546E-2 TWO NORM:1.1319532422608E-2 Statistics: FNS, JACS:183, 35 STEPS, ETF, CTF:77, 3, 0 -T= 0.10000E+01 X(S,TN): -0.58445754991170E-15 0.21706569079431E+00 0.40780040570791E+00 0.55894047714684E+00 0.67056722424815E+00 0.74955212777111E+00 0.80409863830369E+00 0.84125722184744E+00 0.86641102981316E+00 0.88337104837509E+00 0.89477422199390E+00 0.90242422560976E+00 0.90755227028564E+00 0.91150486084567E+00 0.91550801896004E+00 0.92077445074001E+00 0.92854361287370E+00 0.93980818553739E+00 0.95555600033186E+00 0.97609859264019E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP:1 0.99999999999999E+00 0.99915167486587E+00 0.99407749143252E+00 0.99698475698242E+00 0.99847110322787E+00 0.10013005332587E+01 0.10042199615836E+01 0.99925106158264E+00 0.10035485428128E+01 0.10001426793997E+01 0.10025714765328E+01 0.10012085019586E+01 0.85186413971121E+00 0.54287600370401E+00 0.24225328706092E+00 0.10800863019187E+00 0.10040224796535E+00 0.10039561113376E+00 0.10035992330620E+00 0.10017137784193E+00 0.10000000000000E+00 ERR_U: -0.71054273576010E-14 -0.84832513412891E-03 -0.59225085674797E-02 -0.30152430175789E-02 -0.15288967721290E-02 0.13005332586502E-02 0.42199615836367E-02 -0.74893841734891E-03 0.35485444662910E-02 0.14609078360905E-03 0.31485147989585E-02 0.18906229345177E-01 0.28617238632087E-02 0.32639187076953E-01 0.32932764414708E-01 -0.34764476103528E-02 0.49719108810020E-04 0.39339344797318E-03 0.35992145152353E-03 0.17137784174270E-03 0.00000000000000E+00 MAX. NORM:3.2932764414708E-2 TWO NORM:4.5316570225481E-3 Statistics: FNS, JACS:291, 64 STEPS, ETF, CTF:120, 10, 4 C C####################################################################### C C RUNDSH : RUNINF file from single precision version !!! TAU = 1E-3 !!! C for the third example problem !!! in driver !!! C C####################################################################### C Burgers, double wave, eps=0.00100 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.100E-02, KAPPA=.200E+01, ALPHA=.100E-01 Time= 0.65287E-05; H= 0.32643E-05; Order= 1 Time= 0.13057E-04; H= 0.65287E-05; Order= 2 Time= 0.26115E-04; H= 0.13057E-04; Order= 1 Time= 0.52229E-04; H= 0.26115E-04; Order= 1 Time= 0.78344E-04; H= 0.26115E-04; Order= 1 Time= 0.13057E-03; H= 0.52229E-04; Order= 1 Time= 0.17717E-03; H= 0.46598E-04; Order= 1 Time= 0.22377E-03; H= 0.46598E-04; Order= 1 Time= 0.27037E-03; H= 0.46598E-04; Order= 1 Time= 0.31696E-03; H= 0.46598E-04; Order= 1 Time= 0.36356E-03; H= 0.46598E-04; Order= 1 Time= 0.40310E-03; H= 0.39538E-04; Order= 1 Time= 0.44264E-03; H= 0.39538E-04; Order= 1 Time= 0.48218E-03; H= 0.39538E-04; Order= 1 Time= 0.56125E-03; H= 0.79076E-04; Order= 2 Time= 0.64033E-03; H= 0.79076E-04; Order= 2 Time= 0.79848E-03; H= 0.15815E-03; Order= 2 Time= 0.93806E-03; H= 0.13958E-03; Order= 2 Time= 0.10776E-02; H= 0.13958E-03; Order= 2 Time= 0.12172E-02; H= 0.13958E-03; Order= 2 Time= 0.13303E-02; H= 0.11307E-03; Order= 2 Time= 0.14320E-02; H= 0.10176E-03; Order= 2 Time= 0.15338E-02; H= 0.10176E-03; Order= 2 Time= 0.16356E-02; H= 0.10176E-03; Order= 2 Time= 0.17373E-02; H= 0.10176E-03; Order= 1 Time= 0.18391E-02; H= 0.10176E-03; Order= 1 Time= 0.20426E-02; H= 0.20352E-03; Order= 1 Time= 0.22461E-02; H= 0.20352E-03; Order= 1 Time= 0.24497E-02; H= 0.20352E-03; Order= 1 Time= 0.28567E-02; H= 0.40704E-03; Order= 2 Time= 0.32637E-02; H= 0.40704E-03; Order= 2 Time= 0.39268E-02; H= 0.66305E-03; Order= 1 Time= 0.45145E-02; H= 0.58773E-03; Order= 1 Time= 0.56900E-02; H= 0.11755E-02; Order= 1 Time= 0.68654E-02; H= 0.11755E-02; Order= 1 Time= 0.92164E-02; H= 0.23509E-02; Order= 1 Time= 0.11567E-01; H= 0.23509E-02; Order= 1 Time= 0.16269E-01; H= 0.47018E-02; Order= 1 Time= 0.25673E-01; H= 0.94037E-02; Order= 1 Time= 0.35076E-01; H= 0.94037E-02; Order= 1 Time= 0.44480E-01; H= 0.94037E-02; Order= 1 Time= 0.63287E-01; H= 0.18807E-01; Order= 1 Time= 0.80214E-01; H= 0.16927E-01; Order= 1 Time= 0.95352E-01; H= 0.15138E-01; Order= 1 Time= 0.11049E+00; H= 0.15138E-01; Order= 1 Time= 0.12563E+00; H= 0.15138E-01; Order= 1 Time= 0.13973E+00; H= 0.14103E-01; Order= 1 Time= 0.15110E+00; H= 0.11366E-01; Order= 1 Time= 0.16246E+00; H= 0.11366E-01; Order= 1 Time= 0.17383E+00; H= 0.11366E-01; Order= 1 Time= 0.18519E+00; H= 0.11366E-01; Order= 1 Time= 0.20792E+00; H= 0.22732E-01; Order= 2 Time= 0.23066E+00; H= 0.22732E-01; Order= 1 Time= 0.25339E+00; H= 0.22732E-01; Order= 1 Time= 0.26519E+00; H= 0.11805E-01; Order= 1 Time= 0.27452E+00; H= 0.93318E-02; Order= 1 Time= 0.28386E+00; H= 0.93318E-02; Order= 1 Time= 0.29319E+00; H= 0.93318E-02; Order= 1 Time= 0.30252E+00; H= 0.93318E-02; Order= 2 Time= 0.31185E+00; H= 0.93318E-02; Order= 2 Time= 0.32118E+00; H= 0.93318E-02; Order= 1 Time= 0.33985E+00; H= 0.18664E-01; Order= 1 Time= 0.35851E+00; H= 0.18664E-01; Order= 1 Time= 0.37405E+00; H= 0.15540E-01; Order= 1 Time= 0.38959E+00; H= 0.15540E-01; Order= 1 Time= 0.40513E+00; H= 0.15540E-01; Order= 1 Time= 0.41912E+00; H= 0.13986E-01; Order= 1 Time= 0.43310E+00; H= 0.13986E-01; Order= 1 Time= 0.44709E+00; H= 0.13986E-01; Order= 1 Time= 0.46107E+00; H= 0.13986E-01; Order= 2 Time= 0.47506E+00; H= 0.13986E-01; Order= 2 Time= 0.48905E+00; H= 0.13986E-01; Order= 2 Time= 0.50303E+00; H= 0.13986E-01; Order= 2 Time= 0.51702E+00; H= 0.13986E-01; Order= 3 Time= 0.53100E+00; H= 0.13986E-01; Order= 3 Time= 0.54499E+00; H= 0.13986E-01; Order= 2 Time= 0.55758E+00; H= 0.12587E-01; Order= 2 Time= 0.57017E+00; H= 0.12587E-01; Order= 2 Time= 0.58082E+00; H= 0.10654E-01; Order= 2 Time= 0.59147E+00; H= 0.10654E-01; Order= 2 Time= 0.60213E+00; H= 0.10654E-01; Order= 2 Time= 0.61732E+00; H= 0.15190E-01; Order= 2 Time= 0.62745E+00; H= 0.10137E-01; Order= 1 Time= 0.63658E+00; H= 0.91232E-02; Order= 1 Time= 0.64570E+00; H= 0.91232E-02; Order= 1 Time= 0.65482E+00; H= 0.91232E-02; Order= 1 Time= 0.66395E+00; H= 0.91232E-02; Order= 1 Time= 0.68219E+00; H= 0.18246E-01; Order= 2 Time= 0.70044E+00; H= 0.18246E-01; Order= 2 Time= 0.71869E+00; H= 0.18246E-01; Order= 2 Time= 0.71966E+00; H= 0.97011E-03; Order= 2 Time= 0.72160E+00; H= 0.19402E-02; Order= 2 Time= 0.72257E+00; H= 0.97011E-03; Order= 2 Time= 0.72451E+00; H= 0.19402E-02; Order= 2 Time= 0.72839E+00; H= 0.38804E-02; Order= 1 Time= 0.73615E+00; H= 0.77609E-02; Order= 1 Time= 0.74391E+00; H= 0.77609E-02; Order= 1 Time= 0.75943E+00; H= 0.15522E-01; Order= 1 Time= 0.77495E+00; H= 0.15522E-01; Order= 1 Time= 0.79047E+00; H= 0.15522E-01; Order= 1 Time= 0.82152E+00; H= 0.31043E-01; Order= 1 Time= 0.83966E+00; H= 0.18145E-01; Order= 1 Time= 0.85781E+00; H= 0.18145E-01; Order= 1 Time= 0.87595E+00; H= 0.18145E-01; Order= 1 Time= 0.89410E+00; H= 0.18145E-01; Order= 2 Time= 0.91224E+00; H= 0.18145E-01; Order= 2 Time= 0.93039E+00; H= 0.18145E-01; Order= 2 Time= 0.94853E+00; H= 0.18145E-01; Order= 2 Time= 0.96668E+00; H= 0.18145E-01; Order= 2 Time= 0.96693E+00; H= 0.25517E-03; Order= 1 Time= 0.96714E+00; H= 0.20321E-03; Order= 1 Time= 0.96732E+00; H= 0.18289E-03; Order= 1 Time= 0.96750E+00; H= 0.18289E-03; Order= 1 Time= 0.96787E+00; H= 0.36577E-03; Order= 1 Time= 0.96860E+00; H= 0.73154E-03; Order= 1 Time= 0.97006E+00; H= 0.14631E-02; Order= 1 Time= 0.97299E+00; H= 0.29262E-02; Order= 1 Time= 0.97884E+00; H= 0.58524E-02; Order= 1 Time= 0.99055E+00; H= 0.11705E-01; Order= 1 C C####################################################################### C C RESBAK : RESULT file from double precision version C for the first example problem C C####################################################################### C Bakker, Electrodynamics problem; EPS=0.143, P=0.1743, ETA=17.19 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 -T= 0.00000E+00 X(S,TN): 0.00000000000000E+00 0.50000000000000E-01 0.10000000000000E+00 0.15000000000000E+00 0.20000000000000E+00 0.25000000000000E+00 0.30000000000000E+00 0.35000000000000E+00 0.40000000000000E+00 0.45000000000000E+00 0.50000000000000E+00 0.55000000000000E+00 0.60000000000000E+00 0.65000000000000E+00 0.70000000000000E+00 0.75000000000000E+00 0.80000000000000E+00 0.85000000000000E+00 0.90000000000000E+00 0.95000000000000E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 -T= 0.10000E-03 X(S,TN): 0.12735266044843E-20 0.25040639326087E-01 0.56481180725208E-01 0.95013743451470E-01 0.14035700864980E+00 0.19172996726927E+00 0.24805285524386E+00 0.30815424596408E+00 0.37092072417169E+00 0.43536105277879E+00 0.50059964810099E+00 0.56582746220412E+00 0.63023450420058E+00 0.69294260070383E+00 0.75295708822915E+00 0.80916185063231E+00 0.86038575125554E+00 0.90555451801052E+00 0.94389834500290E+00 0.97514972171545E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.97256278198193E+00 0.97297329463441E+00 0.97347359749868E+00 0.97362279770200E+00 0.97365968616696E+00 0.97366795253582E+00 0.97366993754548E+00 0.97367061722011E+00 0.97367094665865E+00 0.97367111095284E+00 0.97367116090313E+00 0.97367110995316E+00 0.97367094676961E+00 0.97367066001102E+00 0.97367048642589E+00 0.97367279233329E+00 0.97369354245866E+00 0.97382236631722E+00 0.97451337030300E+00 0.97805479283087E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 -0.11133568923724E-18 0.21863837076523E-01 0.25474655266945E-01 0.26176978367779E-01 0.26306690020029E-01 0.26327294406898E-01 0.26329526685214E-01 0.26329338687379E-01 0.26329051471724E-01 0.26328889401451E-01 0.26328839463709E-01 0.26328890552885E-01 0.26329056710793E-01 0.26329390777144E-01 0.26330088349518E-01 0.26332151383376E-01 0.26340710275091E-01 0.26378419453056E-01 0.26528830914739E-01 0.27025637086854E-01 0.27429641093465E-01 Statistics: FNS, JACS: 25 9 STEPS, ETF, CTF: 14 0 0 -T= 0.10000E-02 X(S,TN): -0.31906882002238E-17 0.12035734678889E-01 0.27659167677363E-01 0.49865296342561E-01 0.81605227784395E-01 0.12602481635131E+00 0.18619274132530E+00 0.26401844342278E+00 0.35861206116750E+00 0.46490938763530E+00 0.57403998234074E+00 0.67610273839132E+00 0.76369508101800E+00 0.83368289032634E+00 0.88661995793678E+00 0.92509609767101E+00 0.95229372726289E+00 0.97117434284798E+00 0.98419344945419E+00 0.99327637429847E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.84124639823106E+00 0.85198010709681E+00 0.86417807430651E+00 0.86767855422229E+00 0.86870605012885E+00 0.86901606864834E+00 0.86910499263221E+00 0.86912954072521E+00 0.86913888040758E+00 0.86914157449020E+00 0.86913640725412E+00 0.86912565320863E+00 0.86912013739702E+00 0.86915098091298E+00 0.86930686281480E+00 0.86979878730867E+00 0.87108032204927E+00 0.87416885665395E+00 0.88202796056816E+00 0.90698278831326E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 0.27362584056932E-16 0.85805318132295E-01 0.11962496086593E+00 0.12841936075473E+00 0.13028719332919E+00 0.13074916269906E+00 0.13085454149197E+00 0.13086675979615E+00 0.13086128491548E+00 0.13085860096827E+00 0.13086418658332E+00 0.13087854377689E+00 0.13090461599334E+00 0.13096181266530E+00 0.13110841054542E+00 0.13150474101938E+00 0.13256555854283E+00 0.13518001844746E+00 0.14028783863406E+00 0.14665930978927E+00 0.14940965033950E+00 Statistics: FNS, JACS: 61 13 STEPS, ETF, CTF: 33 0 0 -T= 0.10000E-01 X(S,TN): -0.34427396769781E-17 0.16258714721784E-01 0.34382803883098E-01 0.56834581624210E-01 0.87039190267673E-01 0.12957331395931E+00 0.18909073892025E+00 0.26896477224061E+00 0.36925991127282E+00 0.48381263002083E+00 0.60022732075013E+00 0.70517642808932E+00 0.79063665057306E+00 0.85527414673292E+00 0.90186196170236E+00 0.93448224216549E+00 0.95706725596805E+00 0.97276766629829E+00 0.98401678064684E+00 0.99265705857935E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.55402381033045E+00 0.58108980934503E+00 0.63225335776498E+00 0.66627482059999E+00 0.68085510330969E+00 0.68521135327001E+00 0.68607444631980E+00 0.68618620843153E+00 0.68620362725334E+00 0.68620857886650E+00 0.68620572666962E+00 0.68620187972406E+00 0.68622615390488E+00 0.68640891833359E+00 0.68722055551815E+00 0.68983205538279E+00 0.69843451101787E+00 0.72636209309199E+00 0.78483334969053E+00 0.87331834425110E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 0.95184531308424E-17 0.10434520528725E+00 0.18773166403372E+00 0.25316357939666E+00 0.29495931453764E+00 0.31083912490386E+00 0.31358223737728E+00 0.31379490184334E+00 0.31379630801653E+00 0.31379210106119E+00 0.31379642970886E+00 0.31381269708857E+00 0.31387647556126E+00 0.31432320353576E+00 0.31681119642406E+00 0.32390565438164E+00 0.33490067435648E+00 0.34648469633414E+00 0.35618582547805E+00 0.36293333411257E+00 0.36542672394796E+00 Statistics: FNS, JACS: 87 16 STEPS, ETF, CTF: 50 0 0 -T= 0.10000E+00 X(S,TN): -0.39301477256394E-17 0.27509404552255E-01 0.55993690934573E-01 0.86797140010640E-01 0.12184094937080E+00 0.16382419162279E+00 0.21643943774507E+00 0.28414071410633E+00 0.37020645489382E+00 0.47234803523237E+00 0.58046901407967E+00 0.68113067880431E+00 0.76478953875800E+00 0.82907672511573E+00 0.87662241250314E+00 0.91151512663199E+00 0.93755439912681E+00 0.95766078321055E+00 0.97387203296257E+00 0.98760826479254E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.21974581958237E+00 0.24082420330226E+00 0.29058154205529E+00 0.34867209330565E+00 0.40416761691641E+00 0.44973832739684E+00 0.48125563997830E+00 0.49908703254335E+00 0.50698579099418E+00 0.50962248204921E+00 0.51055295173930E+00 0.51203197391951E+00 0.51609497811219E+00 0.52517682893805E+00 0.54436737672286E+00 0.58048304001242E+00 0.63431439688620E+00 0.70289964811670E+00 0.78413725148810E+00 0.87974878778198E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 -0.13624965605258E-15 0.88797777761149E-01 0.16833568476902E+00 0.24183227584845E+00 0.31039173924030E+00 0.37292548234698E+00 0.42566520225675E+00 0.46296774306353E+00 0.48196688573240E+00 0.48823949841194E+00 0.49030549079910E+00 0.49378958448182E+00 0.50305423421003E+00 0.51960830875674E+00 0.54068701843747E+00 0.56194301928120E+00 0.58032835184249E+00 0.59478264507916E+00 0.60534717011268E+00 0.61217164379082E+00 0.61461846804860E+00 Statistics: FNS, JACS: 109 18 STEPS, ETF, CTF: 67 0 0 -T= 0.25000E+00 X(S,TN): -0.77394232436680E-17 0.35291221664463E-01 0.71018431022303E-01 0.10814716025685E+00 0.14806467131394E+00 0.19254335127895E+00 0.24383323005932E+00 0.30463544673108E+00 0.37745820613596E+00 0.46262697494835E+00 0.55547537960931E+00 0.64660274647643E+00 0.72720767170189E+00 0.79352487284645E+00 0.84616067038737E+00 0.88743094489920E+00 0.91981706317539E+00 0.94553072421687E+00 0.96644695048773E+00 0.98413120226406E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.10805705916213E+00 0.12867791899390E+00 0.17698900114014E+00 0.23411718404617E+00 0.29233050707449E+00 0.34784140635393E+00 0.39770957980354E+00 0.43884574066553E+00 0.46883323643915E+00 0.48788864682981E+00 0.50012027062367E+00 0.51181152842142E+00 0.52821211043232E+00 0.55126994712413E+00 0.58088175239822E+00 0.61789338302322E+00 0.66469197252236E+00 0.72340648718939E+00 0.79551786106221E+00 0.88411324464246E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 0.17469927481663E-15 0.74015539998398E-01 0.14091572536753E+00 0.20354613540268E+00 0.26322294010332E+00 0.32010381620710E+00 0.37315588660869E+00 0.41999812692253E+00 0.45728021060632E+00 0.48295040418049E+00 0.50002303997364E+00 0.51592897230737E+00 0.53662083545962E+00 0.56286218700354E+00 0.59169050558857E+00 0.61938043315802E+00 0.64316762431140E+00 0.66177186103287E+00 0.67509370824274E+00 0.68341973830992E+00 0.68632761812349E+00 Statistics: FNS, JACS: 117 19 STEPS, ETF, CTF: 74 0 0 -T= 0.50000E+00 X(S,TN): -0.10401087858425E-16 0.44439151133995E-01 0.88805088552306E-01 0.13391993683124E+00 0.18087852430772E+00 0.23083500485522E+00 0.28495787019539E+00 0.34430963703802E+00 0.40951501036849E+00 0.48017583876915E+00 0.55428244881976E+00 0.62829194501305E+00 0.69829213086099E+00 0.76140020008967E+00 0.81625721438405E+00 0.86267938943143E+00 0.90118650103872E+00 0.93275308192034E+00 0.95869690488395E+00 0.98054836694031E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.61705929604197E-01 0.83571879788228E-01 0.13215155188268E+00 0.18633487608590E+00 0.24042715340552E+00 0.29267601089896E+00 0.34206233746634E+00 0.38753974105531E+00 0.42811989595439E+00 0.46346853064190E+00 0.49467344670541E+00 0.52422258784898E+00 0.55451705126760E+00 0.58639623915570E+00 0.61954797764149E+00 0.65442536646998E+00 0.69380874783919E+00 0.74236196848809E+00 0.80489382030742E+00 0.88669437808147E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 0.65700895428383E-17 0.63742488280905E-01 0.12163930610606E+00 0.17672728262708E+00 0.22997916299074E+00 0.28151559410249E+00 0.33094504614227E+00 0.37748431817190E+00 0.42020724704906E+00 0.45860632934568E+00 0.49330139885287E+00 0.52612438718385E+00 0.55894431980083E+00 0.59231666089018E+00 0.62533815417105E+00 0.65630911076061E+00 0.68338644478598E+00 0.70513627431929E+00 0.72093123514864E+00 0.73076743644006E+00 0.73416693255123E+00 Statistics: FNS, JACS: 125 20 STEPS, ETF, CTF: 80 0 0 -T= 0.10000E+01 X(S,TN): -0.11406215963647E-16 0.54377770873218E-01 0.10808494545177E+00 0.16166526266715E+00 0.21573566831410E+00 0.27077928634383E+00 0.32712495869159E+00 0.38491610794514E+00 0.44407728911349E+00 0.50430112562059E+00 0.56502043001203E+00 0.62539812132548E+00 0.68439946357148E+00 0.74088106716049E+00 0.79366717370613E+00 0.84166550692797E+00 0.88402998991767E+00 0.92037820941479E+00 0.95100850159024E+00 0.97697226217635E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.41855949411223E-01 0.64374253575332E-01 0.11186576458892E+00 0.16204981001984E+00 0.21164684415231E+00 0.26020612617869E+00 0.30762787512131E+00 0.35384101391037E+00 0.39881029175374E+00 0.44257074787550E+00 0.48519358417400E+00 0.52670759824464E+00 0.56703195717810E+00 0.60593811685108E+00 0.64314510985640E+00 0.67890452838048E+00 0.71527252502504E+00 0.75721067809429E+00 0.81192651738417E+00 0.88782965096200E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 -0.44578590086900E-16 0.57131871581142E-01 0.10922405912238E+00 0.15955954423639E+00 0.20880633444811E+00 0.25712191626928E+00 0.30452064222066E+00 0.35096005997028E+00 0.39640086415878E+00 0.44081256300659E+00 0.48416065118635E+00 0.52638435236646E+00 0.56733422813828E+00 0.60668431532277E+00 0.64387209625146E+00 0.67806800042322E+00 0.70817483079002E+00 0.73294885035043E+00 0.75138158024705E+00 0.76298941454337E+00 0.76699670502140E+00 Statistics: FNS, JACS: 134 22 STEPS, ETF, CTF: 87 0 0 -T= 0.20000E+01 X(S,TN): -0.10453487080052E-16 0.60053286165933E-01 0.11903672452853E+00 0.17727603349834E+00 0.23511696218743E+00 0.29279152957340E+00 0.35043580843501E+00 0.40810222875161E+00 0.46575775109282E+00 0.52327762269772E+00 0.58042938272098E+00 0.63684447638083E+00 0.69199386223164E+00 0.74516459050855E+00 0.79546429961772E+00 0.84188923579970E+00 0.88349309414755E+00 0.91966686949829E+00 0.95044808153492E+00 0.97668378749828E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.35153327381863E-01 0.57866852450919E-01 0.10462818533458E+00 0.15300642904687E+00 0.20100812276954E+00 0.24855288696498E+00 0.29567825964121E+00 0.34238444016013E+00 0.38862220583891E+00 0.43429258712398E+00 0.47923390467058E+00 0.52319901522740E+00 0.56583658406214E+00 0.60670229517203E+00 0.64540345319058E+00 0.68213413695708E+00 0.71883592384255E+00 0.76036196145162E+00 0.81407466926679E+00 0.88880159770786E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 0.34573933836692E-18 0.54320861090747E-01 0.10405127525504E+00 0.15262123911497E+00 0.20056434916891E+00 0.24804134438884E+00 0.29511681793596E+00 0.34179520808725E+00 0.38802982418713E+00 0.43372024294874E+00 0.47869664080500E+00 0.52270547185292E+00 0.56538317938318E+00 0.60622870963442E+00 0.64459152942830E+00 0.67964657569350E+00 0.71036894935769E+00 0.73560354154483E+00 0.75438226804794E+00 0.76620785212957E+00 0.77028766323688E+00 Statistics: FNS, JACS: 141 23 STEPS, ETF, CTF: 92 0 0 -T= 0.30000E+01 X(S,TN): -0.13366324572080E-16 0.61545066361672E-01 0.12195026065175E+00 0.18151997567421E+00 0.24056085440098E+00 0.29926752772999E+00 0.35774350631857E+00 0.41601573874462E+00 0.47403668402769E+00 0.53167573923565E+00 0.58870129545288E+00 0.64475511493700E+00 0.69932370370229E+00 0.75171721125178E+00 0.80107729582830E+00 0.84644876003778E+00 0.88695339831125E+00 0.92206688860662E+00 0.95190593494043E+00 0.97735238369153E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.33958735600296E-01 0.56830009133886E-01 0.10362925772185E+00 0.15176446083203E+00 0.19952058657809E+00 0.24686678052552E+00 0.29384678387965E+00 0.34046030294035E+00 0.38665459035630E+00 0.43231821554821E+00 0.47726849921186E+00 0.52123390078984E+00 0.56383968835967E+00 0.60463098717535E+00 0.64324852363152E+00 0.68001330356171E+00 0.71707808141388E+00 0.75938811990011E+00 0.81403088224003E+00 0.88929996809431E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 0.32393540150085E-16 0.53908581777006E-01 0.10328104059902E+00 0.15158886646974E+00 0.19932382877629E+00 0.24663696648239E+00 0.29358884731443E+00 0.34018119462850E+00 0.38636165480727E+00 0.43201871410969E+00 0.47696905690635E+00 0.52093899626580E+00 0.56354236893223E+00 0.60425938926314E+00 0.64241853481305E+00 0.67717432344575E+00 0.70749189089217E+00 0.73224723964890E+00 0.75056561312875E+00 0.76205909614406E+00 0.76602032515102E+00 Statistics: FNS, JACS: 146 24 STEPS, ETF, CTF: 95 0 0 -T= 0.40000E+01 X(S,TN): -0.30297382444938E-16 0.62278095516011E-01 0.12338590729591E+00 0.18362098710431E+00 0.24327345506977E+00 0.30252136489478E+00 0.36145309760915E+00 0.42008213052454E+00 0.47834933356615E+00 0.53611465838921E+00 0.59313957155571E+00 0.64906210077329E+00 0.70336918646940E+00 0.75537732988776E+00 0.80424319346191E+00 0.84903885130975E+00 0.88892830477937E+00 0.92344077295069E+00 0.95274239030673E+00 0.97773675015179E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.33421637963707E-01 0.56380108309802E-01 0.10321818263640E+00 0.15125342893774E+00 0.19890288798807E+00 0.24615558139679E+00 0.29305628330806E+00 0.33960301773953E+00 0.38574027870982E+00 0.43135254308473E+00 0.47625146113157E+00 0.52015841477004E+00 0.56269173428307E+00 0.60339609249792E+00 0.64193678328880E+00 0.67871350581785E+00 0.71600110078959E+00 0.75878544728673E+00 0.81398050607894E+00 0.88957191502355E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 2 -0.16828799093902E-15 0.53737200467624E-01 0.10295749014437E+00 0.15115355821891E+00 0.19879600105626E+00 0.24603030001145E+00 0.29291452768396E+00 0.33944816827416E+00 0.38557604940157E+00 0.43118275023506E+00 0.47607968142906E+00 0.51998627277971E+00 0.56250806145106E+00 0.60311590039048E+00 0.64112763947077E+00 0.67568621693854E+00 0.70575093777841E+00 0.73021688086726E+00 0.74826372716550E+00 0.75956438029934E+00 0.76345721968372E+00 Statistics: FNS, JACS: 147 24 STEPS, ETF, CTF: 96 0 0 C C####################################################################### C C RUNBAK : RUNINF file from double precision version C for the first example problem C C####################################################################### C Bakker, Electrodynamics problem; EPS=0.143, P=0.1743, ETA=17.19 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 Time= 0.20000E-06; H= 0.10000E-06; Order= 1 Time= 0.40000E-06; H= 0.20000E-06; Order= 2 Time= 0.80000E-06; H= 0.40000E-06; Order= 1 Time= 0.16000E-05; H= 0.80000E-06; Order= 1 Time= 0.32000E-05; H= 0.16000E-05; Order= 1 Time= 0.64000E-05; H= 0.32000E-05; Order= 1 Time= 0.12800E-04; H= 0.64000E-05; Order= 1 Time= 0.19200E-04; H= 0.64000E-05; Order= 1 Time= 0.25600E-04; H= 0.64000E-05; Order= 1 Time= 0.38400E-04; H= 0.12800E-04; Order= 2 Time= 0.51200E-04; H= 0.12800E-04; Order= 2 Time= 0.64000E-04; H= 0.12800E-04; Order= 2 Time= 0.76800E-04; H= 0.12800E-04; Order= 2 Time= 0.10240E-03; H= 0.25600E-04; Order= 2 Time= 0.12800E-03; H= 0.25600E-04; Order= 1 Time= 0.15104E-03; H= 0.23040E-04; Order= 1 Time= 0.17408E-03; H= 0.23040E-04; Order= 1 Time= 0.19712E-03; H= 0.23040E-04; Order= 1 Time= 0.24320E-03; H= 0.46080E-04; Order= 2 Time= 0.28928E-03; H= 0.46080E-04; Order= 2 Time= 0.33536E-03; H= 0.46080E-04; Order= 2 Time= 0.38144E-03; H= 0.46080E-04; Order= 2 Time= 0.42752E-03; H= 0.46080E-04; Order= 2 Time= 0.47360E-03; H= 0.46080E-04; Order= 3 Time= 0.51968E-03; H= 0.46080E-04; Order= 2 Time= 0.56576E-03; H= 0.46080E-04; Order= 2 Time= 0.61184E-03; H= 0.46080E-04; Order= 2 Time= 0.65792E-03; H= 0.46080E-04; Order= 2 Time= 0.70400E-03; H= 0.46080E-04; Order= 1 Time= 0.75008E-03; H= 0.46080E-04; Order= 1 Time= 0.84224E-03; H= 0.92160E-04; Order= 1 Time= 0.93440E-03; H= 0.92160E-04; Order= 1 Time= 0.10266E-02; H= 0.92160E-04; Order= 1 Time= 0.12109E-02; H= 0.18432E-03; Order= 2 Time= 0.13952E-02; H= 0.18432E-03; Order= 2 Time= 0.17638E-02; H= 0.36864E-03; Order= 2 Time= 0.20956E-02; H= 0.33178E-03; Order= 2 Time= 0.24274E-02; H= 0.33178E-03; Order= 2 Time= 0.27592E-02; H= 0.33178E-03; Order= 2 Time= 0.30909E-02; H= 0.33178E-03; Order= 2 Time= 0.34227E-02; H= 0.33178E-03; Order= 3 Time= 0.40863E-02; H= 0.66355E-03; Order= 3 Time= 0.47498E-02; H= 0.66355E-03; Order= 3 Time= 0.54134E-02; H= 0.66355E-03; Order= 3 Time= 0.60769E-02; H= 0.66355E-03; Order= 3 Time= 0.67405E-02; H= 0.66355E-03; Order= 2 Time= 0.74040E-02; H= 0.66355E-03; Order= 2 Time= 0.80676E-02; H= 0.66355E-03; Order= 2 Time= 0.87311E-02; H= 0.66355E-03; Order= 2 Time= 0.10058E-01; H= 0.13271E-02; Order= 2 Time= 0.11385E-01; H= 0.13271E-02; Order= 2 Time= 0.12712E-01; H= 0.13271E-02; Order= 2 Time= 0.15367E-01; H= 0.26542E-02; Order= 2 Time= 0.18021E-01; H= 0.26542E-02; Order= 2 Time= 0.20675E-01; H= 0.26542E-02; Order= 2 Time= 0.23329E-01; H= 0.26542E-02; Order= 2 Time= 0.28638E-01; H= 0.53084E-02; Order= 3 Time= 0.33946E-01; H= 0.53084E-02; Order= 3 Time= 0.39255E-01; H= 0.53084E-02; Order= 3 Time= 0.44563E-01; H= 0.53084E-02; Order= 3 Time= 0.49871E-01; H= 0.53084E-02; Order= 3 Time= 0.60488E-01; H= 0.10617E-01; Order= 2 Time= 0.70043E-01; H= 0.95551E-02; Order= 2 Time= 0.79598E-01; H= 0.95551E-02; Order= 2 Time= 0.89154E-01; H= 0.95551E-02; Order= 2 Time= 0.98709E-01; H= 0.95551E-02; Order= 2 Time= 0.11782E+00; H= 0.19110E-01; Order= 3 Time= 0.13693E+00; H= 0.19110E-01; Order= 3 Time= 0.15604E+00; H= 0.19110E-01; Order= 3 Time= 0.17515E+00; H= 0.19110E-01; Order= 3 Time= 0.19426E+00; H= 0.19110E-01; Order= 3 Time= 0.21337E+00; H= 0.19110E-01; Order= 2 Time= 0.23248E+00; H= 0.19110E-01; Order= 2 Time= 0.25159E+00; H= 0.19110E-01; Order= 2 Time= 0.27070E+00; H= 0.19110E-01; Order= 2 Time= 0.30892E+00; H= 0.38221E-01; Order= 2 Time= 0.34714E+00; H= 0.38221E-01; Order= 2 Time= 0.38536E+00; H= 0.38221E-01; Order= 2 Time= 0.42358E+00; H= 0.38221E-01; Order= 2 Time= 0.50003E+00; H= 0.76441E-01; Order= 3 Time= 0.57647E+00; H= 0.76441E-01; Order= 3 Time= 0.65291E+00; H= 0.76441E-01; Order= 3 Time= 0.72935E+00; H= 0.76441E-01; Order= 3 Time= 0.80579E+00; H= 0.76441E-01; Order= 2 Time= 0.88223E+00; H= 0.76441E-01; Order= 2 Time= 0.95867E+00; H= 0.76441E-01; Order= 2 Time= 0.11116E+01; H= 0.15288E+00; Order= 2 Time= 0.12644E+01; H= 0.15288E+00; Order= 2 Time= 0.14173E+01; H= 0.15288E+00; Order= 2 Time= 0.15702E+01; H= 0.15288E+00; Order= 2 Time= 0.18760E+01; H= 0.30576E+00; Order= 3 Time= 0.21817E+01; H= 0.30576E+00; Order= 2 Time= 0.24875E+01; H= 0.30576E+00; Order= 1 Time= 0.27933E+01; H= 0.30576E+00; Order= 1 Time= 0.34048E+01; H= 0.61153E+00; Order= 1 C C####################################################################### C C RESCYL : RESULT file from double precision version C for the second example problem C C####################################################################### C Reaction-diffusion prob. in cyl. coord.; pars: 1.00000 0.00010 1.00000 0.10000 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 -T= 0.00000E+00 X(S,TN): 0.00000000000000E+00 0.50000000000000E-01 0.10000000000000E+00 0.15000000000000E+00 0.20000000000000E+00 0.25000000000000E+00 0.30000000000000E+00 0.35000000000000E+00 0.40000000000000E+00 0.45000000000000E+00 0.50000000000000E+00 0.55000000000000E+00 0.60000000000000E+00 0.65000000000000E+00 0.70000000000000E+00 0.75000000000000E+00 0.80000000000000E+00 0.85000000000000E+00 0.90000000000000E+00 0.95000000000000E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 -T= 0.10000E+00 X(S,TN): 0.29633654800193E-15 0.14518655828625E+00 0.28623613637578E+00 0.41908482419422E+00 0.53995292546954E+00 0.64574851128986E+00 0.73456206846850E+00 0.80600997379943E+00 0.86120451999333E+00 0.90233892710470E+00 0.93209744234193E+00 0.95314566548264E+00 0.96780068468390E+00 0.97792468340331E+00 0.98491427256273E+00 0.98976166077815E+00 0.99315746314550E+00 0.99558125838569E+00 0.99737374380593E+00 0.99878321274549E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.10541347609001E+00 0.10543381112923E+00 0.10542846159353E+00 0.10542697669293E+00 0.10541941101237E+00 0.10539931629053E+00 0.10534688061183E+00 0.10522618072056E+00 0.10497846200468E+00 0.10451695864439E+00 0.10372016041888E+00 0.10243265616718E+00 0.10051987348868E+00 0.97875000660367E-01 0.94308778919243E-01 0.89498639148020E-01 0.82617436086351E-01 0.71961270055454E-01 0.55520963493168E-01 0.32050224112808E-01 0.00000000000000E+00 Statistics: FNS, JACS: 71 14 STEPS, ETF, CTF: 34 1 0 -T= 0.20000E+00 X(S,TN): -0.11792638907364E-15 0.18674250139956E+00 0.36161564535805E+00 0.51532221836835E+00 0.64273309324947E+00 0.74302837364521E+00 0.81863723215575E+00 0.87370797440104E+00 0.91278775931850E+00 0.94000314850915E+00 0.95871185479410E+00 0.97147380412538E+00 0.98015646071269E+00 0.98607515933571E+00 0.99014055601709E+00 0.99298512232870E+00 0.99504830872862E+00 0.99662399106867E+00 0.99789910993335E+00 0.99899464203903E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.22303632049749E+00 0.22309266720346E+00 0.22307397829205E+00 0.22305809941883E+00 0.22301894061950E+00 0.22293445828391E+00 0.22275286764596E+00 0.22239738682208E+00 0.22175946457949E+00 0.22069656329038E+00 0.21903567918989E+00 0.21658529656165E+00 0.21305503122072E+00 0.20760646433304E+00 0.19806940978031E+00 0.18136093968360E+00 0.15639985596911E+00 0.12479179311940E+00 0.88216320484076E-01 0.47050433315259E-01 0.00000000000000E+00 Statistics: FNS, JACS: 80 15 STEPS, ETF, CTF: 40 1 0 -T= 0.30000E+00 X(S,TN): 0.14320554396716E-14 0.20596968998444E+00 0.39457280855472E+00 0.55404257209325E+00 0.68026501628200E+00 0.77520662843622E+00 0.84399823777437E+00 0.89254013062747E+00 0.92617300168885E+00 0.94919203774937E+00 0.96482596838301E+00 0.97540703351966E+00 0.98257232511705E+00 0.98745436043302E+00 0.99084190132803E+00 0.99328242344946E+00 0.99513361215211E+00 0.99661542102899E+00 0.99786362932057E+00 0.99896842313657E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.35555779828961E+00 0.35564085485280E+00 0.35561200548389E+00 0.35558132635160E+00 0.35551206832711E+00 0.35537043764911E+00 0.35508468402543E+00 0.35455395478681E+00 0.35364027460106E+00 0.35216515432253E+00 0.34989560276892E+00 0.34642011011708E+00 0.34044213754871E+00 0.32826236853721E+00 0.30487011125492E+00 0.26953244954386E+00 0.22564377110062E+00 0.17619310916448E+00 0.12248074083887E+00 0.64326526707150E-01 0.00000000000000E+00 Statistics: FNS, JACS: 88 16 STEPS, ETF, CTF: 43 1 0 -T= 0.40000E+00 X(S,TN): 0.17573661222888E-14 0.21714536240210E+00 0.41311648503976E+00 0.57490280278510E+00 0.69958607539812E+00 0.79108933764365E+00 0.85606204614195E+00 0.90120200093970E+00 0.93211312844888E+00 0.95308623239553E+00 0.96725184329120E+00 0.97680747363581E+00 0.98327317844469E+00 0.98770497165375E+00 0.99083765906992E+00 0.99315989881063E+00 0.99497619854938E+00 0.99646998177328E+00 0.99775565086732E+00 0.99891133823822E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.50697530208446E+00 0.50715003288900E+00 0.50709494727959E+00 0.50702558068249E+00 0.50690423986777E+00 0.50668764171967E+00 0.50628342135082E+00 0.50556561168646E+00 0.50436984080349E+00 0.50247956571493E+00 0.49952917267571E+00 0.49441348538268E+00 0.48317911608222E+00 0.45833120911755E+00 0.41655674282601E+00 0.36195417095601E+00 0.29943288273382E+00 0.23180283130867E+00 0.15998075931332E+00 0.83422347369468E-01 0.00000000000000E+00 Statistics: FNS, JACS: 91 16 STEPS, ETF, CTF: 46 1 0 -T= 0.50000E+00 X(S,TN): 0.18445852701699E-14 0.22453039548393E+00 0.42504916702065E+00 0.58784710689971E+00 0.71110879801132E+00 0.80018734147900E+00 0.86268417908266E+00 0.90572840731953E+00 0.93503532905967E+00 0.95485084780955E+00 0.96820343631153E+00 0.97720051578603E+00 0.98329814851021E+00 0.98751582550847E+00 0.99055667647461E+00 0.99286721727617E+00 0.99471537479902E+00 0.99626306865955E+00 0.99761349779020E+00 0.99883914463824E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.68243708640462E+00 0.68277810495631E+00 0.68267873731318E+00 0.68253669913763E+00 0.68232631092308E+00 0.68199779228077E+00 0.68143722816467E+00 0.68048877619805E+00 0.67895569372489E+00 0.67655952419315E+00 0.67260501069311E+00 0.66432549241951E+00 0.64357698297669E+00 0.60148578658400E+00 0.53953838751663E+00 0.46464543953401E+00 0.38206588083428E+00 0.29441901207307E+00 0.20237363383063E+00 0.10508403679625E+00 0.00000000000000E+00 Statistics: FNS, JACS: 96 17 STEPS, ETF, CTF: 48 1 0 -T= 0.60000E+00 X(S,TN): 0.19896455339228E-14 0.22976402276294E+00 0.43337374825586E+00 0.59669864979291E+00 0.71882415309975E+00 0.80614720344578E+00 0.86691611718749E+00 0.90852702796460E+00 0.93674350280112E+00 0.95577029968016E+00 0.96857117148520E+00 0.97719614208978E+00 0.98306587485048E+00 0.98717730441413E+00 0.99019725048412E+00 0.99253472570486E+00 0.99443441614419E+00 0.99604595121440E+00 0.99746635393159E+00 0.99876493793765E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.88950214339158E+00 0.88989698872038E+00 0.88977833151036E+00 0.88958746131439E+00 0.88931080534037E+00 0.88888543558770E+00 0.88817180295746E+00 0.88697659938512E+00 0.88504924113208E+00 0.88196669312571E+00 0.87626925132628E+00 0.86213194539360E+00 0.82693477549876E+00 0.76378695805704E+00 0.67899271247124E+00 0.58116118176215E+00 0.47579308917595E+00 0.36538723369220E+00 0.25037340103839E+00 0.12958244884495E+00 0.00000000000000E+00 Statistics: FNS, JACS: 98 17 STEPS, ETF, CTF: 50 1 0 -T= 0.70000E+00 X(S,TN): 0.19261828521368E-14 0.23377659373911E+00 0.43965276875405E+00 0.60322954622865E+00 0.72436707982107E+00 0.81028614300554E+00 0.86971691780380E+00 0.91023954877469E+00 0.93764119125336E+00 0.95608892373450E+00 0.96849204591115E+00 0.97685680664204E+00 0.98258593401810E+00 0.98666312434109E+00 0.98971246522479E+00 0.99211339722082E+00 0.99409215327768E+00 0.99578855129431E+00 0.99729507715551E+00 0.99867950240365E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.11404669177384E+01 0.11409401761389E+01 0.11407950664162E+01 0.11405304435312E+01 0.11401547215867E+01 0.11395903046279E+01 0.11386658165488E+01 0.11371394869770E+01 0.11346804487025E+01 0.11305978410490E+01 0.11220765449537E+01 0.10990532438480E+01 0.10454763873760E+01 0.95785277553727E+00 0.84631527260672E+00 0.72105095539796E+00 0.58813400082146E+00 0.45020996259660E+00 0.30758753101720E+00 0.15873164955159E+00 0.00000000000000E+00 Statistics: FNS, JACS: 101 17 STEPS, ETF, CTF: 52 1 0 -T= 0.80000E+00 X(S,TN): 0.19489983690457E-14 0.23687484247408E+00 0.44446215799979E+00 0.60818790358613E+00 0.72854965204118E+00 0.81340009981196E+00 0.87181685342508E+00 0.91150890459368E+00 0.93828450007265E+00 0.95628464386745E+00 0.96838244791295E+00 0.97655859879403E+00 0.98219255780115E+00 0.98622833151892E+00 0.98928315863532E+00 0.99172155857119E+00 0.99375914717493E+00 0.99552866915387E+00 0.99711751247974E+00 0.99858952892382E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.14552918110825E+01 0.14558170992759E+01 0.14556539852505E+01 0.14553017251900E+01 0.14547973571279E+01 0.14540405739271E+01 0.14528121711801E+01 0.14507981997373E+01 0.14475251243218E+01 0.14417245515669E+01 0.14279616969269E+01 0.13899339048834E+01 0.13092952664750E+01 0.11892426695586E+01 0.10446088490089E+01 0.88683351366206E+00 0.72182816509103E+00 0.55174921252904E+00 0.37643658786783E+00 0.19392013756469E+00 0.00000000000000E+00 Statistics: FNS, JACS: 109 18 STEPS, ETF, CTF: 54 1 0 -T= 0.90000E+00 X(S,TN): 0.19522004004880E-14 0.23940409202118E+00 0.44830950111163E+00 0.61202518575909E+00 0.73162655965155E+00 0.81551133939449E+00 0.87304550993000E+00 0.91203540705249E+00 0.93829377398775E+00 0.95593275472896E+00 0.96779250259421E+00 0.97583217536967E+00 0.98142304149109E+00 0.98549487874875E+00 0.98862872790646E+00 0.99116713373378E+00 0.99331380665166E+00 0.99519534780138E+00 0.99689620907578E+00 0.99847927530783E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.18703046072040E+01 0.18708707754603E+01 0.18706890057619E+01 0.18702116500391E+01 0.18695124340226E+01 0.18684591699182E+01 0.18667607985324E+01 0.18639914674898E+01 0.18594301761913E+01 0.18507920200978E+01 0.18286960031340E+01 0.17696548106000E+01 0.16548823480591E+01 0.14939893896297E+01 0.13061944743727E+01 0.11048396889746E+01 0.89647985331882E+00 0.68334503881772E+00 0.46501924258866E+00 0.23896237801002E+00 0.00000000000000E+00 Statistics: FNS, JACS: 112 18 STEPS, ETF, CTF: 56 1 0 -T= 0.10000E+01 X(S,TN): 0.19469824500562E-14 0.24148527447510E+00 0.45140991558508E+00 0.61500816141860E+00 0.73387823502942E+00 0.81688810359375E+00 0.87364219573274E+00 0.91202198262112E+00 0.93783931979533E+00 0.95517868798202E+00 0.96685159403756E+00 0.97480014157111E+00 0.98038849859694E+00 0.98453251352016E+00 0.98777877069999E+00 0.99044969249063E+00 0.99273780114691E+00 0.99476373487584E+00 0.99660920760540E+00 0.99833615484976E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.24607685161092E+01 0.24614200363063E+01 0.24611902282900E+01 0.24604728113344E+01 0.24593954922007E+01 0.24577770683979E+01 0.24552004285485E+01 0.24510291540584E+01 0.24440266874217E+01 0.24299089494885E+01 0.23928508777186E+01 0.23004311051512E+01 0.21354741397201E+01 0.19157324556924E+01 0.16663203096580E+01 0.14033722492618E+01 0.11344848770177E+01 0.86199757405020E+00 0.58498494342162E+00 0.29989817369661E+00 0.00000000000000E+00 Statistics: FNS, JACS: 117 18 STEPS, ETF, CTF: 58 1 0 C C####################################################################### C C RUNCYL : RUNINF file from double precision version C for the second example problem C C####################################################################### C Reaction-diffusion prob. in cyl. coord.; pars: 1.00000 0.00010 1.00000 0.10000 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.000E+00, KAPPA=.200E+01, ALPHA=.100E-01 Time= 0.20000E-03; H= 0.10000E-03; Order= 1 Time= 0.40000E-03; H= 0.20000E-03; Order= 2 Time= 0.80000E-03; H= 0.40000E-03; Order= 1 Time= 0.16000E-02; H= 0.80000E-03; Order= 1 Time= 0.32000E-02; H= 0.16000E-02; Order= 1 Time= 0.48000E-02; H= 0.16000E-02; Order= 1 Time= 0.64000E-02; H= 0.16000E-02; Order= 1 Time= 0.96000E-02; H= 0.32000E-02; Order= 2 Time= 0.12480E-01; H= 0.28800E-02; Order= 2 Time= 0.15360E-01; H= 0.28800E-02; Order= 2 Time= 0.18240E-01; H= 0.28800E-02; Order= 2 Time= 0.21120E-01; H= 0.28800E-02; Order= 2 Time= 0.24000E-01; H= 0.28800E-02; Order= 1 Time= 0.26410E-01; H= 0.24103E-02; Order= 1 Time= 0.28821E-01; H= 0.24103E-02; Order= 1 Time= 0.31231E-01; H= 0.24103E-02; Order= 1 Time= 0.33641E-01; H= 0.24103E-02; Order= 1 Time= 0.35811E-01; H= 0.21693E-02; Order= 1 Time= 0.37586E-01; H= 0.17756E-02; Order= 1 Time= 0.39362E-01; H= 0.17756E-02; Order= 1 Time= 0.41138E-01; H= 0.17756E-02; Order= 1 Time= 0.44689E-01; H= 0.35512E-02; Order= 1 Time= 0.48240E-01; H= 0.35512E-02; Order= 1 Time= 0.51791E-01; H= 0.35512E-02; Order= 1 Time= 0.55342E-01; H= 0.35512E-02; Order= 2 Time= 0.58894E-01; H= 0.35512E-02; Order= 2 Time= 0.65996E-01; H= 0.71025E-02; Order= 2 Time= 0.73099E-01; H= 0.71025E-02; Order= 2 Time= 0.80201E-01; H= 0.71025E-02; Order= 2 Time= 0.87303E-01; H= 0.71025E-02; Order= 2 Time= 0.91370E-01; H= 0.40665E-02; Order= 1 Time= 0.95030E-01; H= 0.36599E-02; Order= 1 Time= 0.98690E-01; H= 0.36599E-02; Order= 1 Time= 0.10601E+00; H= 0.73198E-02; Order= 1 Time= 0.11333E+00; H= 0.73198E-02; Order= 1 Time= 0.12065E+00; H= 0.73198E-02; Order= 1 Time= 0.13529E+00; H= 0.14640E-01; Order= 2 Time= 0.14993E+00; H= 0.14640E-01; Order= 2 Time= 0.17921E+00; H= 0.29279E-01; Order= 2 Time= 0.20355E+00; H= 0.24338E-01; Order= 2 Time= 0.22788E+00; H= 0.24338E-01; Order= 2 Time= 0.25222E+00; H= 0.24338E-01; Order= 2 Time= 0.30090E+00; H= 0.48677E-01; Order= 2 Time= 0.34958E+00; H= 0.48677E-01; Order= 2 Time= 0.39825E+00; H= 0.48677E-01; Order= 2 Time= 0.44693E+00; H= 0.48677E-01; Order= 2 Time= 0.49561E+00; H= 0.48677E-01; Order= 3 Time= 0.54428E+00; H= 0.48677E-01; Order= 3 Time= 0.59296E+00; H= 0.48677E-01; Order= 3 Time= 0.64164E+00; H= 0.48677E-01; Order= 3 Time= 0.69031E+00; H= 0.48677E-01; Order= 3 Time= 0.73899E+00; H= 0.48677E-01; Order= 4 Time= 0.78767E+00; H= 0.48677E-01; Order= 3 Time= 0.83634E+00; H= 0.48677E-01; Order= 3 Time= 0.88015E+00; H= 0.43809E-01; Order= 3 Time= 0.92396E+00; H= 0.43809E-01; Order= 3 Time= 0.96777E+00; H= 0.43809E-01; Order= 3 C C####################################################################### C C RESDSH : RESULT file from double precision version !!! TAU = 1E-3 !!! C for the third example problem !!! in driver !!! C C####################################################################### C Burgers, double wave, eps=0.00100 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.100E-02, KAPPA=.200E+01, ALPHA=.100E-01 -T= 0.00000E+00 X(S,TN): 0.00000000000000E+00 0.50000000000000E-01 0.10000000000000E+00 0.15000000000000E+00 0.20000000000000E+00 0.25000000000000E+00 0.30000000000000E+00 0.35000000000000E+00 0.40000000000000E+00 0.45000000000000E+00 0.50000000000000E+00 0.55000000000000E+00 0.60000000000000E+00 0.65000000000000E+00 0.70000000000000E+00 0.75000000000000E+00 0.80000000000000E+00 0.85000000000000E+00 0.90000000000000E+00 0.95000000000000E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.10000000000000E+01 0.10000000000000E+01 0.10000000000000E+01 0.99999999999306E+00 0.99999813668036E+00 0.75000000000000E+00 0.50000186331964E+00 0.50000000000691E+00 0.49999999917554E+00 0.49998184085252E+00 0.30000000000000E+00 0.10001815914748E+00 0.10000000082446E+00 0.10000000000004E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 0.10000000000000E+00 ERR_U: 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 MAX. NORM: 0.0000000000000000E+00 TWO NORM: 0.0000000000000000E+00 -T= 0.25000E+00 X(S,TN): 0.39938631124805E-17 0.10848039902619E+00 0.20332143491505E+00 0.27818744594920E+00 0.33366936812585E+00 0.37291383644095E+00 0.40083196608916E+00 0.42007706567635E+00 0.43538103087761E+00 0.45161358060903E+00 0.47211289543100E+00 0.49608912621524E+00 0.52168938076279E+00 0.54552297753852E+00 0.56985660342795E+00 0.60028529153006E+00 0.64240022494589E+00 0.70136696474965E+00 0.78157647910928E+00 0.88350458954221E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.10000000000000E+01 0.99716089594943E+00 0.10053914674654E+01 0.99398227506464E+00 0.99342130435753E+00 0.10192369473142E+01 0.10241403571050E+01 0.91801071317624E+00 0.70722316658278E+00 0.55195999630692E+00 0.52757210582003E+00 0.55692411740765E+00 0.54507289464643E+00 0.41903177710539E+00 0.24891870363783E+00 0.15397788150532E+00 0.12084641861083E+00 0.10668405272291E+00 0.10148886169492E+00 0.10021053963123E+00 0.10000000000000E+00 ERR_U: 0.22204460492503E-15 -0.28391040505725E-02 0.53914674653861E-02 -0.60177249353576E-02 -0.65786956398048E-02 0.19236995911935E-01 0.24192565874387E-01 -0.75654075692869E-01 -0.10748833391832E+00 0.37702490610937E-01 0.27484839929748E-01 0.56923955738010E-01 0.45082260157957E-01 -0.79870418949233E-01 -0.14574520567546E+00 0.51448279061020E-01 0.20845859175062E-01 0.66840527186798E-02 0.14888616949214E-02 0.21053963123274E-03 0.00000000000000E+00 MAX. NORM: 0.1457452056754566 TWO NORM: 3.6674051387714139E-02 Statistics: FNS, JACS: 122 25 STEPS, ETF, CTF: 54 2 0 -T= 0.55000E+00 X(S,TN): 0.42789669774584E-17 0.16054451804151E+00 0.30092880945903E+00 0.41129713314553E+00 0.49220185168819E+00 0.54915446061045E+00 0.58838172674564E+00 0.61516881937511E+00 0.63346396078613E+00 0.64622568627158E+00 0.65503654061962E+00 0.66206776470849E+00 0.66930854132777E+00 0.67861092376706E+00 0.69195689764799E+00 0.71173453951118E+00 0.74072198769036E+00 0.78231249604778E+00 0.83987086327238E+00 0.91417304003956E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.10000000000000E+01 0.99404766813922E+00 0.99946681627913E+00 0.10044684114696E+01 0.99915737453175E+00 0.99347950474687E+00 0.98418997423471E+00 0.99816960681373E+00 0.10343868913845E+01 0.10199481635346E+01 0.85473686969265E+00 0.55624502985958E+00 0.28655923610120E+00 0.14939763647867E+00 0.10798078391628E+00 0.10887166247564E+00 0.10812640776773E+00 0.10260672751600E+00 0.10090714897772E+00 0.10023518346668E+00 0.10000000000000E+00 ERR_U: 0.00000000000000E+00 -0.59523318607845E-02 -0.53318372086508E-03 0.44684114695528E-02 -0.84262546825287E-03 -0.65204952528811E-02 -0.15810021281136E-01 -0.18267616873753E-02 0.34739699727455E-01 0.28705944538099E-01 -0.63306367878777E-01 -0.69030145673122E-01 0.27645226885963E-01 0.23766155939683E-01 0.61641937601004E-02 0.88367712687488E-02 0.81263018590435E-02 0.26067274901526E-02 0.90714897771901E-03 0.23518346667772E-03 -0.83266726846887E-16 MAX. NORM: 6.9030145673121712E-02 TWO NORM: 1.1360035643140431E-02 Statistics: FNS, JACS: 182 35 STEPS, ETF, CTF: 77 3 0 -T= 0.10000E+01 X(S,TN): 0.65933069367097E-17 0.21712532792970E+00 0.40789355716805E+00 0.55903868093297E+00 0.67065296175650E+00 0.74961920707661E+00 0.80415045798395E+00 0.84129569825018E+00 0.86644124701394E+00 0.88339842283443E+00 0.89479947600615E+00 0.90244623955670E+00 0.90756630387598E+00 0.91151304527626E+00 0.91551636518356E+00 0.92079199808315E+00 0.92855923742497E+00 0.93982088640938E+00 0.95556497937051E+00 0.97610322784590E+00 0.10000000000000E+01 U(X(S,TN),TN), COMP: 1 0.10000000000000E+01 0.99916190570377E+00 0.99405196213500E+00 0.99696282523826E+00 0.99841866007516E+00 0.10014099538875E+01 0.10042543009900E+01 0.99915608628413E+00 0.10036645912492E+01 0.10003563151071E+01 0.10025371199935E+01 0.10011032079500E+01 0.84996071726458E+00 0.53810418710225E+00 0.23683306226127E+00 0.10531371063189E+00 0.10042725788778E+00 0.10040599485127E+00 0.10036314505057E+00 0.10017167622878E+00 0.10000000000000E+00 ERR_U: -0.99920072216264E-15 -0.83809429623427E-03 -0.59480378649983E-02 -0.30371747617424E-02 -0.15813399248433E-02 0.14099538874781E-02 0.42543009900244E-02 -0.84391371584724E-03 0.36645929253346E-02 0.35976877395583E-03 0.31207490251667E-02 0.18973626733526E-01 0.17535496151199E-02 0.28689439130730E-01 0.27872740417935E-01 -0.60821784156097E-02 0.77198024505315E-04 0.40378980423768E-03 0.36314320336787E-03 0.17167622859905E-03 0.83266726846887E-16 MAX. NORM: 2.8689439130729521E-02 TWO NORM: 4.2939725456811341E-03 Statistics: FNS, JACS: 294 62 STEPS, ETF, CTF: 121 4 7 C C####################################################################### C C RUNDSH : RUNINF file from double precision version !!! TAU = 1E-3 !!! C for the third example problem !!! in driver !!! C C####################################################################### C Burgers, double wave, eps=0.00100 MoL, PDE+D&D int.face; DAE int.: DASSL; ID:ACM-TOMS, Ex.I NPTS= 21; RTOL=.100E-02, ATOL=.100E-02 TAU=.100E-02, KAPPA=.200E+01, ALPHA=.100E-01 Time= 0.65287E-05; H= 0.32643E-05; Order= 1 Time= 0.13057E-04; H= 0.65287E-05; Order= 2 Time= 0.26115E-04; H= 0.13057E-04; Order= 1 Time= 0.52229E-04; H= 0.26115E-04; Order= 1 Time= 0.78344E-04; H= 0.26115E-04; Order= 1 Time= 0.13057E-03; H= 0.52229E-04; Order= 1 Time= 0.17717E-03; H= 0.46598E-04; Order= 1 Time= 0.22377E-03; H= 0.46598E-04; Order= 1 Time= 0.27037E-03; H= 0.46598E-04; Order= 1 Time= 0.31696E-03; H= 0.46598E-04; Order= 1 Time= 0.36356E-03; H= 0.46598E-04; Order= 1 Time= 0.40310E-03; H= 0.39538E-04; Order= 1 Time= 0.44264E-03; H= 0.39538E-04; Order= 1 Time= 0.48218E-03; H= 0.39538E-04; Order= 1 Time= 0.56125E-03; H= 0.79077E-04; Order= 2 Time= 0.64033E-03; H= 0.79077E-04; Order= 2 Time= 0.79848E-03; H= 0.15815E-03; Order= 2 Time= 0.93806E-03; H= 0.13958E-03; Order= 2 Time= 0.10776E-02; H= 0.13958E-03; Order= 2 Time= 0.12172E-02; H= 0.13958E-03; Order= 2 Time= 0.13303E-02; H= 0.11307E-03; Order= 2 Time= 0.14320E-02; H= 0.10176E-03; Order= 2 Time= 0.15338E-02; H= 0.10176E-03; Order= 2 Time= 0.16356E-02; H= 0.10176E-03; Order= 2 Time= 0.17373E-02; H= 0.10176E-03; Order= 1 Time= 0.18391E-02; H= 0.10176E-03; Order= 1 Time= 0.20426E-02; H= 0.20353E-03; Order= 1 Time= 0.22462E-02; H= 0.20353E-03; Order= 1 Time= 0.24497E-02; H= 0.20353E-03; Order= 1 Time= 0.28567E-02; H= 0.40705E-03; Order= 2 Time= 0.32638E-02; H= 0.40705E-03; Order= 2 Time= 0.39269E-02; H= 0.66307E-03; Order= 1 Time= 0.45146E-02; H= 0.58775E-03; Order= 1 Time= 0.56901E-02; H= 0.11755E-02; Order= 1 Time= 0.68656E-02; H= 0.11755E-02; Order= 1 Time= 0.92166E-02; H= 0.23510E-02; Order= 1 Time= 0.11568E-01; H= 0.23510E-02; Order= 1 Time= 0.16270E-01; H= 0.47020E-02; Order= 1 Time= 0.25674E-01; H= 0.94040E-02; Order= 1 Time= 0.35078E-01; H= 0.94040E-02; Order= 1 Time= 0.44482E-01; H= 0.94040E-02; Order= 1 Time= 0.63290E-01; H= 0.18808E-01; Order= 1 Time= 0.80217E-01; H= 0.16927E-01; Order= 1 Time= 0.95355E-01; H= 0.15139E-01; Order= 1 Time= 0.11049E+00; H= 0.15139E-01; Order= 1 Time= 0.12563E+00; H= 0.15139E-01; Order= 1 Time= 0.13974E+00; H= 0.14103E-01; Order= 1 Time= 0.15110E+00; H= 0.11364E-01; Order= 1 Time= 0.16247E+00; H= 0.11364E-01; Order= 1 Time= 0.17383E+00; H= 0.11364E-01; Order= 1 Time= 0.18519E+00; H= 0.11364E-01; Order= 1 Time= 0.20792E+00; H= 0.22729E-01; Order= 2 Time= 0.23065E+00; H= 0.22729E-01; Order= 1 Time= 0.25338E+00; H= 0.22729E-01; Order= 1 Time= 0.26519E+00; H= 0.11807E-01; Order= 1 Time= 0.27452E+00; H= 0.93356E-02; Order= 1 Time= 0.28386E+00; H= 0.93356E-02; Order= 1 Time= 0.29319E+00; H= 0.93356E-02; Order= 1 Time= 0.30253E+00; H= 0.93356E-02; Order= 2 Time= 0.31187E+00; H= 0.93356E-02; Order= 2 Time= 0.32120E+00; H= 0.93356E-02; Order= 1 Time= 0.33987E+00; H= 0.18671E-01; Order= 1 Time= 0.35854E+00; H= 0.18671E-01; Order= 1 Time= 0.37410E+00; H= 0.15560E-01; Order= 1 Time= 0.38966E+00; H= 0.15560E-01; Order= 1 Time= 0.40522E+00; H= 0.15560E-01; Order= 1 Time= 0.41923E+00; H= 0.14004E-01; Order= 1 Time= 0.43323E+00; H= 0.14004E-01; Order= 1 Time= 0.44723E+00; H= 0.14004E-01; Order= 1 Time= 0.46124E+00; H= 0.14004E-01; Order= 2 Time= 0.47524E+00; H= 0.14004E-01; Order= 2 Time= 0.48924E+00; H= 0.14004E-01; Order= 2 Time= 0.50325E+00; H= 0.14004E-01; Order= 2 Time= 0.51725E+00; H= 0.14004E-01; Order= 3 Time= 0.53126E+00; H= 0.14004E-01; Order= 3 Time= 0.54526E+00; H= 0.14004E-01; Order= 2 Time= 0.55926E+00; H= 0.14004E-01; Order= 2 Time= 0.57327E+00; H= 0.14004E-01; Order= 2 Time= 0.58515E+00; H= 0.11881E-01; Order= 2 Time= 0.59287E+00; H= 0.77259E-02; Order= 2 Time= 0.60060E+00; H= 0.77259E-02; Order= 2 Time= 0.60832E+00; H= 0.77259E-02; Order= 2 Time= 0.61605E+00; H= 0.77259E-02; Order= 2 Time= 0.61991E+00; H= 0.38629E-02; Order= 2 Time= 0.62378E+00; H= 0.38629E-02; Order= 2 Time= 0.62691E+00; H= 0.31327E-02; Order= 2 Time= 0.63317E+00; H= 0.62655E-02; Order= 1 Time= 0.64571E+00; H= 0.12531E-01; Order= 1 Time= 0.65671E+00; H= 0.11008E-01; Order= 1 Time= 0.66772E+00; H= 0.11008E-01; Order= 1 Time= 0.67873E+00; H= 0.11008E-01; Order= 1 Time= 0.70075E+00; H= 0.22017E-01; Order= 2 Time= 0.72276E+00; H= 0.22017E-01; Order= 2 Time= 0.74478E+00; H= 0.22017E-01; Order= 2 Time= 0.76680E+00; H= 0.22017E-01; Order= 2 Time= 0.78534E+00; H= 0.18547E-01; Order= 1 Time= 0.80389E+00; H= 0.18547E-01; Order= 1 Time= 0.82244E+00; H= 0.18547E-01; Order= 1 Time= 0.84099E+00; H= 0.18547E-01; Order= 1 Time= 0.85953E+00; H= 0.18547E-01; Order= 1 Time= 0.87808E+00; H= 0.18547E-01; Order= 1 Time= 0.87814E+00; H= 0.65204E-04; Order= 1 Time= 0.87827E+00; H= 0.13041E-03; Order= 1 Time= 0.87838E+00; H= 0.10282E-03; Order= 1 Time= 0.87848E+00; H= 0.10282E-03; Order= 1 Time= 0.87869E+00; H= 0.20564E-03; Order= 1 Time= 0.87889E+00; H= 0.20564E-03; Order= 1 Time= 0.87930E+00; H= 0.41127E-03; Order= 1 Time= 0.88013E+00; H= 0.82255E-03; Order= 1 Time= 0.88177E+00; H= 0.16451E-02; Order= 1 Time= 0.88259E+00; H= 0.82255E-03; Order= 1 Time= 0.88424E+00; H= 0.16451E-02; Order= 1 Time= 0.88753E+00; H= 0.32902E-02; Order= 1 Time= 0.89411E+00; H= 0.65804E-02; Order= 1 Time= 0.90727E+00; H= 0.13161E-01; Order= 1 Time= 0.92043E+00; H= 0.13161E-01; Order= 1 Time= 0.93359E+00; H= 0.13161E-01; Order= 1 Time= 0.95991E+00; H= 0.26322E-01; Order= 2 Time= 0.98623E+00; H= 0.26322E-01; Order= 2 Time= 0.99216E+00; H= 0.59224E-02; Order= 2 8<------------------------------------------------------------------------- C####################################################################### C C Source code TOMS submission `A Moving-Grid Interface for Systems of C One-Dimensional Time-Dependent Partial Differential Equations' by C J.G. Blom and P.A. Zegeling. C C First the single precision version then, separated by a C C*********** line, the double precision version C C*********************************************************************** C C Single Precision files C C*********************************************************************** C C Contains, separated by a C######## line, the following files: C ------------------------------------------------------------ C PRBBAK : problem dependent routines for first example problem C PRBCYL : problem dependent routines for second example problem C PRBDSH : problem dependent routines for third example problem C (Burgers' equation) C DRIVER : test program to use the moving-grid interface in a DASSL C environment C SPMDIF : moving-grid interface routines C MACHAR : MACHAR routine from W.J. Cody C (available from Netlib: send machar from elefunt) C SDASSL : DASSL DAE integrator from L.R. Petzold C (available from Netlib: send sdassl from ode) C NB. DASSL needs the following files: C DASUSE : contains the routine C I1MACH to get the standard error message unit (6). C (also available from Netlib: send i1mach from core) C R1MACH to determine machine precision, uses value determined C by MACHAR C (also available from Netlib: send r1mach from core) C and the dummies for the routines SGEFA and SGESL from LINPACK C (available from Netlib: send sgefa/sgesl from linpack) C DASLIP : LINPACK routines needed by DASSL C (available from Netlib: send sgbfa/sgbsl from linpack) C C C Of the next three problem dependent files only one should be loaded C C####################################################################### C C PRBBAK : problem dependent routines for first example problem C C####################################################################### C SUBROUTINE INIPRB (TEXT) CHARACTER TEXT*80 C C Initialize /PROBLM/ C INTEGER NPDE, NPRINT LOGICAL ANAJAC, SOLAV REAL XL, XR, T0, TE REAL DUMPRO(5), TPRINT(10) COMMON /PROBLM/ NPDE, XL, XR, T0, TE, DUMPRO, + ANAJAC, SOLAV, TPRINT, NPRINT C INTEGER M REAL EPS, P, ETA DATA EPS /0.143/, ETA /17.19/, P /0.1743/ C NPDE = 2 M = 0 XL = 0.0 XR = 1.0 T0 = 0.0 TE = 4.0 ANAJAC = .FALSE. SOLAV = .FALSE. NPRINT = 10 TPRINT(1) = 1.0E-4 TPRINT(2) = 1.0E-3 TPRINT(3) = 1.0E-2 TPRINT(4) = 0.1 TPRINT(5) = 0.25 TPRINT(6) = 0.5 TPRINT(7) = 1.0 TPRINT(8) = 2.0 TPRINT(9) = 3.0 TPRINT(10) = 4.0 TEXT = ' Bakker, Electrodynamics problem' WRITE(TEXT(33:80),'(6H; EPS=,F5.3,4H, P=,F6.4,6H, ETA=,F5.2)') + EPS, P, ETA DUMPRO(1) = M DUMPRO(2) = EPS DUMPRO(3) = P DUMPRO(4) = ETA RETURN END SUBROUTINE UINIT (NPDE, NPTS, Y) C C Routine for PDE initial values. C Entry: C Y(NPDE+1,i) = x_i; uniform mesh, generated by package C Exit: C Y(NPDE+1,i) = x_i; mesh, optionally changed by user C Y( k,i) = u_k(x_i,t0); initial value of k-th component C i = 1,.., NPTS C INTEGER NPDE, NPTS REAL Y(NPDE+1,NPTS) INTEGER I DO 10 I = 1, NPTS Y(1,I) = 1.0 Y(2,I) = 0.0 10 CONTINUE RETURN END SUBROUTINE SPDEF (T, X, NPDE, U, DUDX, C, Q, R, IRES) C C Routine to describe the body of the PDE system. C The PDE is written as C NPDE k -m m C sum C (x,t,u,u ) u + Q (x,t,u,u ) = x (x R (x,t,u,u ) ) C k=1 jk x t j x j x x C the functions C, Q and R must be defined in this routine. C INTEGER NPDE, IRES REAL T, X REAL U(NPDE), DUDX(NPDE), C(NPDE,NPDE), Q(NPDE), R(NPDE) INTEGER J, K REAL EPS, ETA, GZ, P, Z DATA EPS /0.143/, ETA /17.19/, P /0.1743/ DO 10 K = 1, NPDE DO 20 J = 1, NPDE C(J,K) = 0.0 20 CONTINUE C(K,K) = 1.0 10 CONTINUE Z = U(1) - U(2) GZ = EXP(ETA*Z/3) - EXP(-2*ETA*Z/3) Q(1) = GZ Q(2) = -GZ R(1) = EPS*P * DUDX(1) R(2) = P * DUDX(2) RETURN END SUBROUTINE BNDR (T, BETA, GAMMA, U, DUDX, NPDE, LEFT, IRES) C C Boundary conditions routine C The boundary conditions are written as C BETA (x,t) R (x,t,u,u ) = GAMMA (x,t,u,u ) C j j x j x C The functions BETA and GAMMA should be defined in this routine. C INTEGER NPDE, IRES LOGICAL LEFT REAL T REAL BETA(NPDE), GAMMA(NPDE), U(NPDE), DUDX(NPDE) IF (LEFT) THEN BETA (1) = 1.0 GAMMA(1) = 0.0 BETA (2) = 0.0 GAMMA(2) = U(2) ELSE BETA (1) = 0.0 GAMMA(1) = U(1) - 1.0 BETA (2) = 1.0 GAMMA(2) = 0.0 ENDIF RETURN END SUBROUTINE UEXACT (X, T, U) REAL X, T REAL U(*) C RETURN END C C####################################################################### C C PRBCYL : problem dependent routines for second example problem C C####################################################################### C SUBROUTINE INIPRB (TEXT) CHARACTER TEXT*80 C C Initialize /PROBLM/ C INTEGER NPDE, NPRINT LOGICAL ANAJAC, SOLAV REAL XL, XR, T0, TE REAL DUMPRO(5), TPRINT(10) COMMON /PROBLM/ NPDE, XL, XR, T0, TE, DUMPRO, + ANAJAC, SOLAV, TPRINT, NPRINT C INTEGER I, M REAL ALPHA, BETA, GAMMA, EPS C NPDE = 1 M = 1 XL = 0.0 XR = 1.0 T0 = 0.0 TE = 1.0 ANAJAC = .FALSE. SOLAV = .FALSE. NPRINT = 10 DO 10 I = 1, NPRINT TPRINT(I) = 0.1*I 10 CONTINUE ALPHA = 1.0 BETA = 0.0001 GAMMA = 1.0 EPS = 0.1 TEXT = ' Reaction-diffusion prob. in cyl. coord.; pars:' WRITE(TEXT(48:80),'(4F8.5)') ALPHA, BETA, GAMMA, EPS DUMPRO(1) = M DUMPRO(2) = ALPHA DUMPRO(3) = BETA DUMPRO(4) = GAMMA DUMPRO(5) = EPS RETURN END SUBROUTINE UINIT (NPD, NPTS, Y) C C Routine for PDE initial values. C Entry: C Y(NPDE+1,i) = x_i; uniform mesh, generated by package C Exit: C Y(NPDE+1,i) = x_i; mesh, optionally changed by user C Y( k,i) = u_k(x_i,t0); initial value of k-th component C i = 1,.., NPTS C INTEGER NPD, NPTS REAL Y(NPDE+1,NPTS) C INTEGER NPDE, NPRINT LOGICAL ANAJAC, SOLAV REAL XL, XR, T0, TE REAL DUMPRO(5), TPRINT(10) COMMON /PROBLM/ NPDE, XL, XR, T0, TE, DUMPRO, + ANAJAC, SOLAV, TPRINT, NPRINT C INTEGER I DO 10 I = 1, NPTS Y(1,I) = 0.0 10 CONTINUE RETURN END SUBROUTINE SPDEF (T,X, NPD, U, DUDX, C, Q, R, IRES) C C Routine to describe the body of the PDE system. C The PDE is written as C NPDE k -m m C sum C (x,t,u,u ) u + Q (x,t,u,u ) = x (x R (x,t,u,u ) ) C k=1 jk x t j x j x x C the functions C, Q and R must be defined in this routine. C INTEGER NPD, IRES REAL T, X REAL U(NPDE), DUDX(NPDE), C(NPDE,NPDE), Q(NPDE), R(NPDE) C INTEGER NPDE, NPRINT LOGICAL ANAJAC, SOLAV REAL XL, XR, T0, TE REAL DUMPRO(5), TPRINT(10) COMMON /PROBLM/ NPDE, XL, XR, T0, TE, DUMPRO, + ANAJAC, SOLAV, TPRINT, NPRINT REAL ALPHA, BETA, GAMMA, EPS C ALPHA = DUMPRO(2) BETA = DUMPRO(3) GAMMA = DUMPRO(4) EPS = DUMPRO(5) C(1,1) = ALPHA Q(1) = -GAMMA*EXP(U(1)/(1+EPS*U(1))) R(1) = BETA*DUDX(1) RETURN END SUBROUTINE BNDR (T, BETA, GAMMA, U, DUDX, NPD, LEFT, IRES) C C Boundary conditions routine C The boundary conditions are written as C BETA (x,t) R (x,t,u,u ) = GAMMA (x,t,u,u ) C j j x j x C The functions BETA and GAMMA should be defined in this routine. C INTEGER NPD, IRES LOGICAL LEFT REAL T REAL BETA(NPDE), GAMMA(NPDE), U(NPDE), DUDX(NPDE) C INTEGER NPDE, NPRINT LOGICAL ANAJAC, SOLAV REAL XL, XR, T0, TE REAL DUMPRO(5), TPRINT(10) COMMON /PROBLM/ NPDE, XL, XR, T0, TE, DUMPRO, + ANAJAC, SOLAV, TPRINT, NPRINT C IF (LEFT) THEN BETA(1) = 1.0 GAMMA(1) = 0.0 ELSE BETA(1) = 0.0 GAMMA(1) = U(1) - 0.0 ENDIF RETURN END SUBROUTINE UEXACT (X, T, U) C C Exact solution C REAL X, T REAL U(*) RETURN END C C####################################################################### C C PRBDSH : problem dependent routines for third example problem C (Burgers' equation) C C#####################################################################