/* nag_pde_parab_1d_fd (d03pcc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include #include static void pdedef(Integer, double, double, const double[], const double[], double[], double[], double[], Integer *, Nag_Comm *); static void bndary(Integer, double, const double[], const double[], Integer, double[], double[], Integer *, Nag_Comm *); static int uinit(double *, double *, Integer, Integer, double); # define U(I,J) u[npde*((J)-1)+(I)-1] # define P(I,J) p[npde*((J)-1)+(I)-1] # define UOUT(I,J,K) uout[npde*(intpts*((K)-1)+(J)-1)+(I)-1] int main(void) { const Integer npts=20, npde=2, neqn=npts*npde, intpts=6, itype=1, nwk=(10+6*npde)*neqn, lisave=neqn+24, lrsave=nwk+(21+3*npde)*npde+7*npts+54; Integer exit_status, 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; /* 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)) ) { Vprintf("Allocation failure\n"); exit_status = 1; goto END; } INIT_FAIL(fail); exit_status = 0; Vprintf("d03pcc Example Program Results\n\n"); 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 = piby2/19; x[0] = 0.0; x[19] = 1.0; for (i = 1; i < 19; ++i) { x[i] = sin(hx*i); } /* Set initial conditions */ ts = 0.0; tout = 1e-5; Vprintf("Accuracy requirement = %12.5f\n", acc); Vprintf("Parameter alpha = %12.3f\n\n",alpha); Vprintf(" t / x "); for (i = 0; i < 6; ++i) { Vprintf("%8.4f", xout[i]); Vprintf((i+1)%6 == 0 || i == 5 ?"\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 */ d03pcc(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) { Vprintf("Error from d03pcc.\n%s\n", fail.message); exit_status = 1; goto END; } /* Interpolate at required spatial points */ d03pzc(npde, m, u, npts, x, xout, intpts, 1, uout, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from d03pzc.\n%s\n", fail.message); exit_status = 1; goto END; } Vprintf("\n %6.4f u(1)", tout); for (i = 1; i <= 6; ++i) { Vprintf("%8.4f", UOUT(1,i,1)); Vprintf(i%6 == 0 || i == 6 ?"\n":""); } Vprintf(" u(2)"); for (i = 1; i <= 6; ++i) { Vprintf("%8.4f", UOUT(2,i,1)); Vprintf(i%6 == 0 || i == 6 ?"\n":""); } } /* Print integration statistics */ Vprintf("\n"); Vprintf(" Number of integration steps in time "); Vprintf("%4ld\n",isave[0]); Vprintf(" Number of residual evaluations of resulting ODE system "); Vprintf("%4ld\n",isave[1]); Vprintf(" Number of Jacobian evaluations "); Vprintf("%4ld\n",isave[2]); Vprintf(" Number of iterations of nonlinear solver "); Vprintf("%4ld\n",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 uinit(double *u, double *x, Integer npde, Integer npts, double alpha) { /* PDE initial conditon */ Integer i; for (i = 1; i <= npts; ++i) { U(1,i) = alpha*2.0*x[i-1]; U(2,i) = 1.0; } return 0; } static void 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; q[0] = *alpha*4.0*(u[1]+x*ux[1]); q[1] = 0.0; r[0] = x*ux[0]; r[1] = ux[1] - u[0] * u[1]; P(1, 1) = 0.0; P(1, 2) = 0.0; P(2, 1) = 0.0; P(2, 2) = 1.0-x*x; return; } static void 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) { beta[0] = 0.0; beta[1] = 1.0; gamma[0] = u[0]; gamma[1] = -u[0]*u[1]; } else { beta[0] = 1.0; beta[1] = 0.0; gamma[0] = -u[0]; gamma[1] = u[1]; } return; }