/* nag_pde_parab_1d_fd_ode (d03phc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. */ #include #include #include #include #include static void pdedef(Integer, double, double, const double[], const double[], Integer, const double[], const double[], double[], double[], double[], Integer *, Nag_Comm *); static void bndary(Integer, double, const double[], const double[], Integer, const double[], const double[], Integer, double[], double[], Integer *, Nag_Comm *); static void odedef(Integer, double, Integer, const double[], const double[], Integer, const double[], const double[], const double[], const double[], const double[], const double[], double[], Integer *, Nag_Comm *); static void uvinit(Integer, Integer, double *, double *, Integer, Integer, double); static void exact(double, Integer, double *, double *); #define P(I,J) p[npde*((J)-1)+(I)-1] #define UCPX(I,J) ucpx[npde*((J)-1)+(I)-1] #define UCP(I,J) ucp[npde*((J)-1)+(I)-1] int main(void) { const Integer npde=1, npts=21, ncode=1, m=0, nxi=1, neqn=npde*npts+ncode, lisave=24, lenode=11*neqn+50, nwkres=npde*(npts+6*nxi+3*npde+15)+ncode+nxi+7*npts+2, lrsave=neqn*neqn+neqn+nwkres+lenode; double tout, ts; Integer exit_status, i, ind, it, itask, itol, itrace; Nag_Boolean theta; double *algopt=0, *atol=0, *exy=0, *rsave=0, *rtol=0, *u=0, *x=0, *xi=0; Integer *isave=0; NagError fail; Nag_Comm comm; Nag_D03_Save saved; /* Allocate memory */ if ( !(algopt = NAG_ALLOC(30, double)) || !(atol = NAG_ALLOC(1, double)) || !(exy = NAG_ALLOC(npts, double)) || !(rsave = NAG_ALLOC(lrsave, double)) || !(rtol = NAG_ALLOC(1, double)) || !(u = NAG_ALLOC(neqn, double)) || !(x = NAG_ALLOC(npts, double)) || !(xi = NAG_ALLOC(1, double)) || !(isave = NAG_ALLOC(lisave, Integer)) ) { Vprintf("Allocation failure\n"); exit_status = 1; goto END; } Vprintf("nag_pde_parab_1d_fd_ode (d03phc) Example Program Results\n\n"); INIT_FAIL(fail); exit_status = 0; itrace = 0; itol = 1; atol[0] = 1e-4; rtol[0] = atol[0]; Vprintf(" Simple coupled PDE using BDF\n"); Vprintf(" Accuracy requirement =%10.3e", atol[0]); Vprintf(" Number of points = %4ld\n\n", npts); /* Set break-points */ for (i = 0; i < npts; ++i) { x[i] = i/(npts-1.0); } xi[0] = 1.0; ind = 0; itask = 1; /* Set theta = 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; /* Loop over output value of t */ ts = 1e-4; tout = 0.0; Vprintf(" 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, npde, neqn, ts); for (it = 0; it < 5; ++it) { tout = 0.1*pow(2.0, (it+1.0)); /* nag_pde_parab_1d_fd_ode (d03phc). * General system of parabolic PDEs, coupled DAEs, method of * lines, finite differences, one space variable */ nag_pde_parab_1d_fd_ode(npde, m, &ts, tout, pdedef, bndary, u, npts, x, 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) { Vprintf("Error from nag_pde_parab_1d_fd_ode (d03phc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Check against the exact solution */ exact(tout, npts, x, exy); Vprintf(" t = %6.3f\n", ts); Vprintf(" App. sol. %7.3f%9.3f%9.3f%9.3f%9.3f", u[0], u[4], u[8], u[12], u[20]); Vprintf(" ODE sol. =%8.3f\n", u[21]); Vprintf(" Exact sol. %7.3f%9.3f%9.3f%9.3f%9.3f", exy[0], exy[4], exy[8], exy[12], exy[20]); Vprintf(" ODE sol. =%8.3f\n\n", ts); } Vprintf(" Number of integration steps in time = %6ld\n", isave[0]); Vprintf(" Number of function evaluations = %6ld\n", isave[1]); Vprintf(" Number of Jacobian evaluations =%6ld\n", isave[2]); Vprintf(" Number of iterations = %6ld\n\n", isave[4]); END: 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 pdedef(Integer npde, double t, double x, const double u[], const double ux[], Integer ncode, const double v[], const double vdot[], double p[], double q[], double r[], Integer *ires, Nag_Comm *comm) { P(1, 1) = v[0] * v[0]; r[0] = ux[0]; q[0] = -(x) * ux[0] * v[0] * vdot[0]; return; } static void bndary(Integer npde, double t, const double u[], const double ux[], Integer ncode, const double v[], const double vdot[], Integer ibnd, double beta[], double gamma[], Integer *ires, Nag_Comm *comm) { beta[0] = 1.0; if (ibnd == 0) { gamma[0] = -v[0]*exp(t); } else { gamma[0] = -v[0]*vdot[0]; } return; } static void 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 rcp[], const double ucpt[], const double ucptx[], double f[], Integer *ires, Nag_Comm *comm) { if (*ires == 1) { f[0] = vdot[0] - v[0] * UCP(1, 1) - UCPX(1, 1) - 1.0 - t; } else if (*ires == -1) { f[0] = vdot[0]; } return; } static void uvinit(Integer npde, Integer npts, double *x, double *u, Integer ncode, Integer neqn, double ts) { /* Routine for PDE initial values */ Integer i; for (i = 0; i < npts; ++i) { u[i] = exp(ts*(1.0 - x[i])) - 1.0; } u[neqn-1] = ts; return; } static void exact(double time, Integer npts, double *x, double *u) { /* Exact solution (for comparison purpose) */ Integer i; for (i = 0; i < npts; ++i) { u[i] = exp(time*(1.0 - x[i])) - 1.0; } return; }