/* nag_pde_parab_1d_keller_ode (d03pkc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. */ #include #include #include #include #include #include #ifdef __cplusplus extern "C" { #endif static void NAG_CALL pdedef(Integer, double, double, const double[], const double[], const double[], Integer, const double[], const double[], double[], Integer *, Nag_Comm *); static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc, const double u[], const double ut[], Integer ncode, const double v[], const double vdot[], double res[], Integer *ires, Nag_Comm *comm); static void NAG_CALL odedef(Integer, double, Integer, const double[], const double[], Integer, const double[], const double[], const double[], const double[], double[], Integer *, Nag_Comm *); static void NAG_CALL uvinit(Integer npde, Integer npts, double *x, double *u, Integer ncode, Integer neqn, double ts); static void NAG_CALL exact(double, Integer, Integer, double *, double *); #ifdef __cplusplus } #endif #define UCP(I, J) ucp[npde*((J) -1)+(I) -1] int main(int argc, char *argv[]) { FILE *fpout; const Integer npde = 2, npts = 21, ncode = 1, nxi = 1, nleft = 1; const Integer neqn = npde*npts+ncode, lisave = 24; const Integer nwkres = npde*(npts+6*nxi+3*npde+15)+ncode+nxi+7*npts+2; const Integer lenode = 11*neqn+50, lrsave = neqn*neqn+neqn+nwkres+lenode; double tout, ts; Integer exit_status = 0, i, ind, it, itask, itol, itrace; Nag_Boolean theta; double *algopt = 0, *atol = 0, *exy = 0, *rsave = 0, *rtol = 0; double *u = 0, *x = 0, *xi = 0; Integer *isave = 0; NagError fail; Nag_Comm comm; Nag_D03_Save saved; INIT_FAIL(fail); /* Check for command-line IO options */ fpout = nag_example_file_io(argc, argv, "-results", NULL); fprintf(fpout, "nag_pde_parab_1d_keller_ode (d03pkc) Example Program Results\n\n"); /* Allocate memory */ if (!(algopt = NAG_ALLOC(30, double)) || !(atol = NAG_ALLOC(1, double)) || !(exy = NAG_ALLOC(neqn, double)) || !(rsave = NAG_ALLOC(lrsave, double)) || !(rtol = NAG_ALLOC(1, double)) || !(u = NAG_ALLOC(neqn, double)) || !(x = NAG_ALLOC(npts, double)) || !(xi = NAG_ALLOC(nxi, double)) || !(isave = NAG_ALLOC(lisave, Integer))) { fprintf(fpout, "Allocation failure\n"); exit_status = 1; goto END; } itrace = 0; itol = 1; atol[0] = 1e-4; rtol[0] = atol[0]; fprintf(fpout, " Accuracy requirement =%12.3e", atol[0]); fprintf(fpout, " Number of points = %3ld\n\n", npts); /* Set spatial-mesh points */ for (i = 0; i < npts; ++i) x[i] = i/(npts-1.0); xi[0] = 1.0; ind = 0; itask = 1; /* Set THETA to TRUE if the Theta integrator is required */ theta = Nag_FALSE; for (i = 0; i < 30; ++i) algopt[i] = 0.0; if (theta) { algopt[0] = 2.0; } else { algopt[0] = 0.0; } algopt[0] = 1.0; algopt[12] = 0.005; /* Loop over output value of t */ ts = 1e-4; tout = 0.0; fprintf(fpout, " x %9.3f%9.3f%9.3f%9.3f%9.3f\n\n", x[0], x[4], x[8], x[12], x[20]); uvinit(npde, npts, x, u, ncode, neqn, ts); for (it = 0; it < 5; ++it) { tout = 0.1*pow(2.0, (it+1.0)); /* nag_pde_parab_1d_keller_ode (d03pkc). * General system of first-order PDEs, coupled DAEs, method * of lines, Keller box discretisation, one space variable */ nag_pde_parab_1d_keller_ode(npde, &ts, tout, pdedef, bndary, u, npts, x, nleft, ncode, odedef, nxi, xi, neqn, rtol, atol, itol, Nag_TwoNorm, Nag_LinAlgFull, algopt, rsave, lrsave, isave, lisave, itask, itrace, 0, &ind, &comm, &saved, &fail); if (fail.code != NE_NOERROR) { fprintf(fpout, "Error from nag_pde_parab_1d_keller_ode (d03pkc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Check against the exact solution */ exact(tout, neqn, npts, x, exy); fprintf(fpout, " t = %6.3f\n", ts); fprintf(fpout, " App. sol. %7.3f%9.3f%9.3f%9.3f%9.3f", u[0], u[8], u[16], u[24], u[40]); fprintf(fpout, " ODE sol. =%8.3f\n", u[42]); fprintf(fpout, " Exact sol. %7.3f%9.3f%9.3f%9.3f%9.3f", exy[0], exy[8], exy[16], exy[24], exy[40]); fprintf(fpout, " ODE sol. =%8.3f\n\n", ts); } fprintf(fpout, " Number of integration steps in time = %6ld\n", isave[0]); fprintf(fpout, " Number of function evaluations = %6ld\n", isave[1]); fprintf(fpout, " Number of Jacobian evaluations =%6ld\n", isave[2]); fprintf(fpout, " Number of iterations = %6ld\n\n", isave[4]); END: if (fpout != stdout) fclose(fpout); if (algopt) NAG_FREE(algopt); if (atol) NAG_FREE(atol); if (exy) NAG_FREE(exy); if (rsave) NAG_FREE(rsave); if (rtol) NAG_FREE(rtol); if (u) NAG_FREE(u); if (x) NAG_FREE(x); if (xi) NAG_FREE(xi); if (isave) NAG_FREE(isave); return exit_status; } static void NAG_CALL uvinit(Integer npde, Integer npts, double *x, double *u, Integer ncode, Integer neqn, double ts) { Integer i, k; /* Routine for PDE initial values */ k = 0; for (i = 0; i < npts; ++i) { u[k] = exp(ts*(1.0-x[i])) - 1.0; u[k+1] = -ts *exp(ts *(1.0-x[i])); k += 2; } u[neqn-1] = ts; return; } static void NAG_CALL odedef(Integer npde, double t, Integer ncode, const double v[], const double vdot[], Integer nxi, const double xi[], const double ucp[], const double ucpx[], const double ucpt[], double f[], Integer *ires, Nag_Comm *comm) { if (*ires == -1) { f[0] = vdot[0]; } else { f[0] = vdot[0] - v[0]*UCP(1, 1) - UCP(2, 1) - 1.0 - t; } return; } static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[], const double ut[], const double ux[], Integer ncode, const double v[], const double vdot[], double res[], Integer *ires, Nag_Comm *comm) { if (*ires == -1) { res[0] = v[0]*v[0]*ut[0] - x*u[1]* v[0]*vdot[0]; res[1] = 0.0; } else { res[0] = v[0]*v[0]*ut[0] - x*u[1]* v[0]*vdot[0] - ux[1]; res[1] = u[1] - ux[0]; } return; } static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc, const double u[], const double ut[], Integer ncode, const double v[], const double vdot[], double res[], Integer *ires, Nag_Comm *comm) { if (ibnd == 0) { if (*ires == -1) { res[0] = 0.0; } else { res[0] = u[1] + v[0]* exp(t); } } else { if (*ires == -1) { res[0] = v[0]* vdot[0 ]; } else { res[0] = u[1] + v[0]* vdot[0 ]; } } return; } static void NAG_CALL exact(double time, Integer neqn, Integer npts, double *x, double *u) { /* Exact solution (for comparison purposes) */ Integer i, k; k = 0; for (i = 0; i < npts; ++i) { u [k] = exp(time* (1.0-x[i])) - 1.0; k += 2; } return; }