```/* nag_ode_ivp_rkts_errass (d02puc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.2, 2017.
*/
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd02.h>

#ifdef __cplusplus
extern "C"
{
#endif
static void NAG_CALL f(double t, Integer n, const double *y,
double *yp, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

#define N 4

int main(void)
{
/* Scalars */
Integer exit_status = 0;
Integer liwsav, lrwsav, lwcomm, n;
double errmax, hnext, hstart, tend, terrmx, tgot, tol, tstart, twant, waste;
Integer fevals, j, k, stepcost, stepsok;
/* Arrays */
static double ruser[1] = { -1.0 };
double *rmserr = 0, *rwsav = 0, *thresh = 0, *wcomm = 0;
double *ygot = 0, *yinit = 0, *ymax = 0, *ypgot = 0;
Integer *iwsav = 0;
char nag_enum_arg[40];
/* NAG types */
NagError fail;
Nag_RK_method method;
Nag_ErrorAssess errass;
Nag_Comm comm;

INIT_FAIL(fail);

n = N;
liwsav = 130;
lrwsav = 350 + 32 * n;
lwcomm = 6 * n;

printf("nag_ode_ivp_rkts_errass (d02puc) Example Program Results\n\n");

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

if (!(rmserr = NAG_ALLOC(n, double)) ||
!(thresh = NAG_ALLOC(n, double)) ||
!(ygot = NAG_ALLOC(n, double)) ||
!(yinit = NAG_ALLOC(n, double)) ||
!(ymax = NAG_ALLOC(n, double)) ||
!(ypgot = NAG_ALLOC(n, double)) ||
!(wcomm = NAG_ALLOC(lwcomm, double)) ||
!(rwsav = NAG_ALLOC(lrwsav, double)) ||
!(iwsav = NAG_ALLOC(liwsav, Integer))
)
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Skip heading in data file */
scanf("%*[^\n] ");

/* Set initial conditions for ODE and parameters for the integrator. */
scanf(" %39s%*[^\n] ", nag_enum_arg);
/* nag_enum_name_to_value (x04nac) Converts NAG enum member name to value. */
method = (Nag_RK_method) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n] ", nag_enum_arg);
errass = (Nag_ErrorAssess) nag_enum_name_to_value(nag_enum_arg);
scanf("%lf%lf%*[^\n] ", &tstart, &tend);

for (j = 0; j < n; j++)
scanf("%lf", &yinit[j]);
scanf("%*[^\n] ");
scanf("%lf%lf%*[^\n] ", &hstart, &tol);
for (j = 0; j < n; j++)
scanf("%lf", &thresh[j]);
scanf("%*[^\n] ");

/* Initialize Runge-Kutta method for integrating ODE using
* nag_ode_ivp_rkts_setup (d02pqc).
*/
nag_ode_ivp_rkts_setup(n, tstart, tend, yinit, tol, thresh, method,
errass, hstart, iwsav, rwsav, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_ivp_rkts_setup (d02pqc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

printf(" Calculation with tol = %8.1e\n", tol);
printf("    t          y1        y1'\n");
printf("%6.3f", tstart);
for (k = 0; k < n; k++)
printf("   %8.4f", yinit[k]);
printf("\n");

twant = tend;
tgot = tstart;
while (tgot < twant) {
/* Solve ODE by Runge-Kutta method up to next time increment using
* nag_ode_ivp_rkts_range (d02pec).
*/
nag_ode_ivp_rkts_range(f, n, twant, &tgot, ygot, ypgot, ymax, &comm,
iwsav, rwsav, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_ivp_rkts_range (d02pec).\n%s\n",
fail.message);
exit_status = 2;
goto END;
}

printf("%6.3f", tgot);
for (k = 0; k < n; k++)
printf("   %8.4f", ygot[k]);
printf("\n");

}

/* Compute and print error estimates using
* nag_ode_ivp_rkts_errass (d02puc).
*/
nag_ode_ivp_rkts_errass(n, rmserr, &errmax, &terrmx, iwsav, rwsav, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_ivp_rkts_errass (d02puc).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}

printf("\n Componentwise error assessment\n");
printf("       ");
for (j = 0; j < n; j++)
printf("%11.2e", rmserr[j]);

printf("\n\n Worst global error observed was %9.2e", errmax);
printf(" - occuring at t = %6.3f\n\n", terrmx);

/* Get diagnostics on whole integration using
* nag_ode_ivp_rkts_diag (d02ptc).
*/
nag_ode_ivp_rkts_diag(&fevals, &stepcost, &waste, &stepsok, &hnext, iwsav,
rwsav, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ode_ivp_rkts_diag (d02ptc).\n%s\n", fail.message);
exit_status = 4;
goto END;
}
printf(" Cost of the integration in evaluations of f is %6" NAG_IFMT "\n\n",
fevals);

END:
NAG_FREE(rmserr);
NAG_FREE(thresh);
NAG_FREE(ygot);
NAG_FREE(yinit);
NAG_FREE(ymax);
NAG_FREE(ypgot);
NAG_FREE(rwsav);
NAG_FREE(iwsav);
NAG_FREE(wcomm);
return exit_status;
}

static void NAG_CALL f(double t, Integer n, const double *y, double *yp,
Nag_Comm *comm)
{
double r;

if (comm->user[0] == -1.0) {
printf("(User-supplied callback f, first invocation.)\n");
comm->user[0] = 0.0;
}
r = sqrt(y[0] * y[0] + y[1] * y[1]);
r = r * r * r;

yp[0] = y[2];
yp[1] = y[3];
yp[2] = -y[0] / r;
yp[3] = -y[1] / r;
}
```