/* nag_pde_parab_1d_fd (d03pcc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. * Mark 7b revised, 2004. * Mark 23 revised, 2011. */ #include #include #include #include #include #include #include #ifdef __cplusplus extern "C" { #endif static void NAG_CALL pdedef(Integer, double, double, const double[], const double[], double[], double[], double[], Integer *, Nag_Comm *); static void NAG_CALL bndary(Integer, double, const double[], const double[], Integer, double[], double[], Integer *, Nag_Comm *); static int NAG_CALL uinit(double *, double *, Integer, Integer, double); #ifdef __cplusplus } #endif int main(void) { const Integer npts = 20, npde = 2, neqn = npts*npde, intpts = 6, itype = 1; const Integer nwk = (10+6*npde)*neqn, lisave = neqn+24; const Integer lrsave = nwk+(21+3*npde)*npde+7*npts+54; Integer exit_status = 0, i, ind, it, itask, itrace, m; double acc, alpha, hx, piby2, tout, ts; double xout[6] = { 0., .4, .6, .8, .9, 1. }; double *rsave = 0, *u = 0, *uout = 0, *x = 0; Integer *isave = 0; NagError fail; Nag_Comm comm; Nag_D03_Save saved; INIT_FAIL(fail); printf("nag_pde_parab_1d_fd (d03pcc) Example Program Results\n\n"); /* Allocate memory */ if (!(rsave = NAG_ALLOC(lrsave, double)) || !(u = NAG_ALLOC(npde*npts, double)) || !(uout = NAG_ALLOC(npde*intpts*itype, double)) || !(x = NAG_ALLOC(npts, double)) || !(isave = NAG_ALLOC(lisave, Integer))) { printf("Allocation failure\n"); exit_status = 1; goto END; } acc = 0.001; m = 1; itrace = 0; alpha = 1.0; comm.p = (Pointer)α ind = 0; itask = 1; /* Set spatial mesh points */ piby2 = 0.5*nag_pi; hx = piby2/((double)(npts-1)); x[0] = 0.0; x[npts-1] = 1.0; for (i = 1; i < npts-1; ++i) x[i] = sin(hx*i); /* Set initial conditions */ ts = 0.0; tout = 1e-5; printf("Accuracy requirement = %12.5f\n", acc); printf("Parameter alpha = %10.3f\n\n", alpha); printf(" t / x "); for (i = 0; i < intpts; ++i) printf("%8.4f", xout[i]); printf("\n"); /* Set the initial values */ uinit(u, x, npde, npts, alpha); for (it = 0; it < 5; ++it) { tout *= 10.0; /* Solve for next iteration step using * nag_pde_parab_1d_fd (d03pcc). * General system of parabolic PDEs, method of lines, finite * differences, one space variable */ nag_pde_parab_1d_fd(npde, m, &ts, tout, pdedef, bndary, u, npts, x, acc, rsave, lrsave, isave, lisave, itask, itrace, 0, &ind, &comm, &saved, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_pde_parab_1d_fd (d03pcc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Interpolate at required spatial points using * nag_pde_interp_1d_fd (d03pzc). * PDEs, spatial interpolation fo use with the suite of routines * nag_pde_parab_1d (d03p). */ nag_pde_interp_1d_fd(npde, m, u, npts, x, xout, intpts, 1, uout, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_pde_interp_1d_fd (d03pzc).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\n %6.4f u(1)", tout); for (i = 0; i < intpts; ++i) printf("%8.4f", uout[npde*i]); printf("\n %6s u(2)",""); for (i = 0; i < intpts; ++i) printf("%8.4f", uout[npde*i+1]); printf("\n"); } /* Print integration statistics */ printf("\n %-55s%4ld\n", "Number of integration steps in time", isave[0]); printf(" %-55s%4ld\n", "Number of residual evaluations of" " resulting ODE system", isave[1]); printf(" %-55s%4ld\n", "Number of Jacobian evaluations", isave[2]); printf(" %-55s%4ld\n", "Number of iterations of nonlinear solver", isave[4]); END: if (rsave) NAG_FREE(rsave); if (u) NAG_FREE(u); if (uout) NAG_FREE(uout); if (x) NAG_FREE(x); if (isave) NAG_FREE(isave); return exit_status; } static int NAG_CALL uinit(double *u, double *x, Integer npde, Integer npts, double alpha) { Integer i; /* Intial conditions for u1 */ for (i = 0; i < npts; ++i) u[i*npde] = alpha*2.0*x[i]; /* Intial conditions for u2 */ for (i = 0; i < npts; ++i) u[i*npde+1] = 1.0; return 0; } static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[], const double ux[], double p[], double q[], double r[], Integer *ires, Nag_Comm *comm) { /* PDE coefficients */ double *alpha = (double *) comm->p; /* Coefficients on first PDE */ q[0] = *alpha*4.0*(u[1]+x*ux[1]); r[0] = x*ux[0]; p[0] = 0.0; p[npde] = 0.0; /* Coefficients on first PDE */ q[1] = 0.0; r[1] = ux[1] - u[0] * u[1]; p[1] = 0.0; p[1+npde] = 1.0-x*x; return; } static void NAG_CALL bndary(Integer npde, double t, const double u[], const double ux[], Integer ibnd, double beta[], double gamma[], Integer *ires, Nag_Comm *comm) { /* Boundary conditions */ if (ibnd == 0) { /* u[0] = 0 */ beta[0] = 0.0; gamma[0] = u[0]; /* ux[1] = 0 ==> 1.0*r[1] = ux[1] - u[0]*u[1] = -u[0]*u[1] */ beta[1] = 1.0; gamma[1] = -u[0]*u[1]; } else { /* d(x*u[0])/dx = x*ux[0] + u[0] = 0 */ beta[0] = 1.0; gamma[0] = -u[0]; /* u[1] = 0 */ beta[1] = 0.0; gamma[1] = u[1]; } return; }