Example description
/* nag_pde_parab_1d_fd_ode (d03phc) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 */

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd03.h>

#ifdef __cplusplus
extern "C"
{
#endif
  static void NAG_CALL pdedef(Integer, double, double, const double[],
                              const double[], Integer, const double[],
                              const double[], double[], double[], double[],
                              Integer *, Nag_Comm *);
  static void NAG_CALL bndary(Integer, double, const double[], const double[],
                              Integer, const double[], const double[],
                              Integer, double[], double[], Integer *,
                              Nag_Comm *);
  static void NAG_CALL 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 NAG_CALL uvinit(Integer, Integer, double *, double *, Integer,
                              Integer, double);
#ifdef __cplusplus
}
#endif

#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)
{
  /* Constants */
  const Integer print_stat = 0;
  const Integer npde = 1, npts = 121, ncode = 1, m = 0, nxi = 1;
  const Integer neqn = npde*npts + ncode;
  const Integer lisave = 24, lenode = 11*neqn + 50;
  const Integer nwkres = neqn + npde*(6*nxi + 3*npde + 15) + nxi + 7*npts + 2;
  const Integer lrsave = neqn*neqn + neqn + nwkres + lenode;
  static double ruser[3] = { -1.0, -1.0, -1.0 };

  /* Scalars */
  double        tout, ts;
  Integer       exit_status = 0, i, ind, it, itask, itol, itrace;

  /* Arrays */
  double        *algopt = 0, *atol = 0, *rsave = 0, *rtol = 0;
  double        *u = 0, *x = 0, *xi = 0;
  Integer       *isave = 0;

  /* Nag Types */
  NagError      fail;
  Nag_Boolean   theta;
  Nag_Comm      comm;
  Nag_D03_Save  saved;

  INIT_FAIL(fail);

  printf("nag_pde_parab_1d_fd_ode (d03phc) Example Program Results\n\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

  /* Allocate memory */

  if (!(algopt = NAG_ALLOC(30, double)) ||
      !(atol = NAG_ALLOC(1, 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)))
  {
    printf("Allocation failure\n");
    exit_status = 1;
    goto END;
  }

  itrace = 0;
  itol = 1;
  atol[0] = 1e-6;
  rtol[0] = atol[0];

  /* 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 */

  printf("  Simple coupled PDE using BDF\n");
  printf("  Accuracy requirement =%12.3e", atol[0]);
  printf(" Number of points = %4" NAG_IFMT "\n\n", npts);
  printf("%7s%8s%s\n", "time", "", "solution at x=0");

  ts = 1e-4;
  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) {
      printf("Error from nag_pde_parab_1d_fd_ode (d03phc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    printf("%7.1f%15s%6.2f\n", ts, "", u[0]);
  }
  if (print_stat) {
    printf(" Number of integration steps in time = %6" NAG_IFMT "\n", isave[0]);
    printf(" Number of function evaluations = %6" NAG_IFMT "\n", isave[1]);
    printf(" Number of Jacobian evaluations =%6" NAG_IFMT "\n", isave[2]);
    printf(" Number of iterations = %6" NAG_IFMT "\n\n", isave[4]);
  }
END:
  NAG_FREE(algopt);
  NAG_FREE(atol);
  NAG_FREE(rsave);
  NAG_FREE(rtol);
  NAG_FREE(u);
  NAG_FREE(x);
  NAG_FREE(xi);
  NAG_FREE(isave);

  return exit_status;
}

static void NAG_CALL 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)
{
  if (comm->user[0] == -1.0) {
    /* printf("(User-supplied callback pdedef, first invocation.)\n"); */
    comm->user[0] = 0.0;
  }
  P(1, 1) = v[0] * v[0];
  r[0] = ux[0];
  q[0] = -(x) * ux[0] * v[0] * vdot[0];

  return;
}

static void NAG_CALL 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)
{
  if (comm->user[1] == -1.0) {
    /* printf("(User-supplied callback bndary, first invocation.)\n"); */
    comm->user[1] = 0.0;
  }
  beta[0] = 1.0;
  if (ibnd == 0) {
    gamma[0] = -v[0] * exp(t);
  }
  else {
    gamma[0] = -v[0] * vdot[0];
  }
  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 rcp[], const double ucpt[],
                            const double ucptx[], double f[], Integer *ires,
                            Nag_Comm *comm)
{
  if (comm->user[2] == -1.0) {
    /* printf("(User-supplied callback odedef, first invocation.)\n"); */
    comm->user[2] = 0.0;
  }
  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 NAG_CALL 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;
}