NAG Library Manual, Mark 28.4
```/* nag_ode_ivp_adams_interp (d02qzc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.4, 2022.
*
*/

#include <nag.h>
#include <stdio.h>

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL ftry03(Integer neqf, double x, const double y[],
double yp[], Nag_User *comm);
#ifdef __cplusplus
}
#endif

#define NEQF 2
#define TSTART 0.0

int main(void) {
static Integer use_comm[1] = {1};
Nag_Boolean alter_g, crit, one_step, sophist, vectol;
Integer exit_status = 0, i, j, max_step, neqf, neqg, nwant;
NagError fail;
Nag_Start state;
Nag_User comm;
double *atol = 0, hmax, pi, *rtol = 0, t, tcrit, tinc, tout, twant, *y = 0;
double *ypwant = 0, *ywant = 0;

INIT_FAIL(fail);

/* For communication with user-supplied functions: */
comm.p = (Pointer)&use_comm;

/* nag_math_pi (x01aac).
* pi
*/
pi = nag_math_pi;
state = Nag_NewStart;
neqf = NEQF;
if (neqf >= 1) {
if (!(atol = NAG_ALLOC(neqf, double)) ||
!(rtol = NAG_ALLOC(neqf, double)) || !(y = NAG_ALLOC(neqf, double)) ||
!(ywant = NAG_ALLOC(neqf, double)) ||
!(ypwant = NAG_ALLOC(neqf, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
} else {
exit_status = 1;
return exit_status;
}

neqg = 0;
sophist = Nag_FALSE;
vectol = Nag_TRUE;
for (i = 0; i < 2; ++i) {
atol[i] = 1e-08;
rtol[i] = 0.0001;
}
one_step = Nag_TRUE;
crit = Nag_TRUE;
tinc = pi * 0.0625;
tcrit = tinc * 8.0;
tout = tcrit;
max_step = 500;
hmax = 2.0;
t = TSTART;
twant = TSTART + tinc;
nwant = 2;
y[0] = 0.0;
y[1] = 1.0;
printf("\n   T        Y(1)    Y(2)\n");
printf(" %6.4f   %7.4f %7.4f  \n", t, y[0], y[1]);

* Setup function for nag_ode_ivp_adams_roots (d02qfc)
*/
nag_ode_ivp_adams_setup(&state, neqf, vectol, atol, rtol, one_step, crit,
tcrit, hmax, max_step, neqg, &alter_g, sophist, &opt,
&fail);
if (fail.code != NE_NOERROR) {
exit_status = 1;
goto END;
}

j = 1;

while (t < tout && fail.code == NE_NOERROR) {
* Ordinary differential equation solver using Adams method
* (sophisticated use)
*/
nag_ode_ivp_adams_roots(neqf, ftry03, &t, y, tout, NULLDFN, &comm, &opt,
&fail);
if (fail.code != NE_NOERROR) {
fail.message);
exit_status = 1;
goto END;
}

while (twant <= t && fail.code == NE_NOERROR) {
* Interpolation function for use with
*/
nag_ode_ivp_adams_interp(neqf, twant, nwant, ywant, ypwant, &opt, &fail);
if (fail.code != NE_NOERROR) {
fail.message);
exit_status = 1;
goto END;
}

printf(" %6.4f   %7.4f %7.4f  \n", twant, ywant[0], ywant[1]);
++j;
twant = (double)j * tinc + 0.0;
}
}
/* Free the memory which was allocated by
* nag_ode_ivp_adams_setup (d02qwc) to the pointers inside opt.
*/
* Freeing function for use with nag_ode_ivp_adams_roots
* (d02qfc)
*/

END:
NAG_FREE(atol);
NAG_FREE(rtol);
NAG_FREE(y);
NAG_FREE(ywant);
NAG_FREE(ypwant);
return exit_status;
}

static void NAG_CALL ftry03(Integer neqf, double x, const double y[],
double yp[], Nag_User *comm) {
Integer *use_comm = (Integer *)comm->p;

if (use_comm[0]) {
printf("(User-supplied callback ftry03, first invocation.)\n");
use_comm[0] = 0;
}

yp[0] = y[1];
yp[1] = -y[0];
} /* ftry03 */
```