```/* nag_pde_parab_1d_coll (d03pdc) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd03.h>
#include <nagx01.h>

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

#define U(I, J)       u[npde*((J) -1)+(I) -1]
#define UOUT(I, J, K) uout[npde*(intpts*((K) -1)+(J) -1)+(I) -1]
#define P(I, J, K)    p[npde*(npde*((K) -1)+(J) -1)+(I) -1]
#define Q(I, J)       q[npde*((J) -1)+(I) -1]
#define R(I, J)       r[npde*((J) -1)+(I) -1]
#define UX(I, J)      ux[npde*((J) -1)+(I) -1]

int main(void)
{
const Integer nbkpts = 10, nelts = nbkpts - 1, npde = 2, npoly = 3,
m = 0, itype = 1, npts = nelts * npoly + 1, neqn = npde * npts,
intpts = 6, npl1 = npoly + 1, lisave = neqn + 24,
mu = npde * (npoly + 1) - 1, lenode = (3 * mu + 1) * neqn,
nwkres =
3 * npl1 * npl1 + npl1 * (npde * npde + 6 * npde + nbkpts + 1)
+ 13 * npde + 5, lrsave = 11 * neqn + 50 + nwkres + lenode;

static double ruser[3] = { -1.0, -1.0, -1.0 };
static double xout[6] = { -1., -.6, -.2, .2, .6, 1. };
double acc, tout, ts;
Integer exit_status = 0, i, ind, it, itask, itrace;

double *rsave = 0, *u = 0, *uout = 0, *x = 0, *xbkpts = 0;
Integer *isave = 0;
NagError fail;
Nag_Comm comm;
Nag_D03_Save saved;

INIT_FAIL(fail);

printf("nag_pde_parab_1d_coll (d03pdc) Example Program Results\n\n");

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

/* 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)) ||
!(xbkpts = NAG_ALLOC(nbkpts, double)) ||
!(isave = NAG_ALLOC(lisave, Integer)))
{
printf("Allocation failure\n");
exit_status = 1;
goto END;
}

acc = 1e-4;
itrace = 0;

/* Set the break-points */

for (i = 0; i < 10; ++i) {
xbkpts[i] = i * 2.0 / 9.0 - 1.0;
}

ind = 0;
ts = 0.0;
tout = 1e-5;
printf(" Polynomial degree =%4" NAG_IFMT "", npoly);
printf("   No. of elements = %4" NAG_IFMT "\n\n", nelts);
printf(" Accuracy requirement = %12.3e", acc);
printf("  Number of points = %5" NAG_IFMT "\n\n", npts);
printf("  t /   x   ");

for (i = 0; i < 6; ++i) {
printf("%8.4f", xout[i]);
printf((i + 1) % 6 == 0 || i == 5 ? "\n" : "");
}
printf("\n");

/* Loop over output values of t */

for (it = 0; it < 5; ++it) {
tout *= 10.0;

/* nag_pde_parab_1d_coll (d03pdc).
* General system of parabolic PDEs, method of lines,
* Chebyshev C^0 collocation, one space variable
*/
nag_pde_parab_1d_coll(npde, m, &ts, tout, pdedef, bndary, u, nbkpts,
xbkpts, npoly, npts, x, uinit, acc, rsave, lrsave,
isave, lisave, itask, itrace, 0, &ind, &comm,
&saved, &fail);

if (fail.code != NE_NOERROR) {
printf("Error from nag_pde_parab_1d_coll (d03pdc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Interpolate at required spatial points */

/* nag_pde_interp_1d_coll (d03pyc).
* PDEs, spatial interpolation with nag_pde_parab_1d_coll
* (d03pdc) or nag_pde_parab_1d_coll_ode (d03pjc)
*/
nag_pde_interp_1d_coll(npde, u, nbkpts, xbkpts, npoly, npts, xout,
intpts, itype, uout, rsave, lrsave, &fail);

if (fail.code != NE_NOERROR) {
printf("Error from nag_pde_interp_1d_coll (d03pyc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\n %6.4f u(1)", tout);

for (i = 1; i <= 6; ++i) {
printf("%8.4f", UOUT(1, i, 1));
printf(i % 6 == 0 || i == 6 ? "\n" : "");
}

printf("        u(2)");

for (i = 1; i <= 6; ++i) {
printf("%8.4f", UOUT(2, i, 1));
printf(i % 6 == 0 || i == 6 ? "\n" : "");
}
}

/* Print integration statistics */

printf("\n");
printf(" Number of integration steps in time                    ");
printf("%4" NAG_IFMT "\n", isave[0]);
printf(" Number of residual evaluations of resulting ODE system ");
printf("%4" NAG_IFMT "\n", isave[1]);
printf(" Number of Jacobian evaluations                         ");
printf("%4" NAG_IFMT "\n", isave[2]);
printf(" Number of iterations of nonlinear solver               ");
printf("%4" NAG_IFMT "\n", isave[4]);

END:
NAG_FREE(rsave);
NAG_FREE(u);
NAG_FREE(uout);
NAG_FREE(x);
NAG_FREE(xbkpts);
NAG_FREE(isave);

return exit_status;
}

static void NAG_CALL uinit(Integer npde, Integer npts, const double x[],
double u[], Nag_Comm *comm)
{
Integer i;
double piby2;

if (comm->user[0] == -1.0) {
printf("(User-supplied callback uinit, first invocation.)\n");
comm->user[0] = 0.0;
}
piby2 = 0.5 * nag_pi;
for (i = 1; i <= npts; ++i) {
U(1, i) = -sin(piby2 * x[i - 1]);
U(2, i) = -piby2 * piby2 * U(1, i);
}
return;
}

static void NAG_CALL pdedef(Integer npde, double t, const double x[],
Integer nptl, const double u[], const double ux[],
double p[], double q[], double r[], Integer *ires,
Nag_Comm *comm)
{
Integer i;

if (comm->user[1] == -1.0) {
printf("(User-supplied callback pdedef, first invocation.)\n");
comm->user[1] = 0.0;
}
for (i = 1; i <= nptl; ++i) {
Q(1, i) = U(2, i);
Q(2, i) = U(1, i) * UX(2, i) - UX(1, i) * U(2, i);
R(1, i) = UX(1, i);
R(2, i) = UX(2, i);
P(1, 1, i) = 0.0;
P(1, 2, i) = 0.0;
P(2, 1, i) = 0.0;
P(2, 2, i) = 1.0;
}
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)
{
if (comm->user[2] == -1.0) {
printf("(User-supplied callback bndary, first invocation.)\n");
comm->user[2] = 0.0;
}
if (ibnd == 0) {
beta[0] = 1.0;
gamma[0] = 0.0;
beta[1] = 0.0;
gamma[1] = u[0] - 1.0;
}
else {
beta[0] = 1.0;
gamma[0] = 0.0;
beta[1] = 0.0;
gamma[1] = u[0] + 1.0;
}
return;
}
```