NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```/* D02PT_P0W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

#include <iostream>
#include <math.h>
#include <nag.h>
#include <nagad.h>
#include <stdio.h>
using namespace std;

#ifdef __cplusplus
extern "C"
{
#endif
static void NAG_CALL f(void *&        ad_handle,
const double & t,
const Integer &n,
const double   y[],
double         yp[],
Integer        iuser[],
double         ruser[]);
#ifdef __cplusplus
}
#endif

int main(void)
{
const Integer n      = 2;
const Integer liwsav = 130;
const Integer lrwsav = 350 + 32 * n;

Integer exit_status = 0;

double * rwsav = 0, *thresh = 0, *ynow = 0;
double * ypnow = 0, *y = 0, ruser[2];
Integer *iwsav = 0, iuser[1];

cout << "D02PT_P0W_F C++ Header Example Program Results\n\n";

thresh = new double[n];
ynow   = new double[n];
y      = new double[n];
ypnow  = new double[n];
iwsav  = new Integer[liwsav];
rwsav  = new double[lrwsav];

// Set initial conditions for ODE and parameters for the integrator.
Integer method = 2;
double  tol, hstart, tend, tstart;
tstart    = 0.0;
tol       = 1.0e-4;
tend      = 2.0 * nag_math_pi;
y[0]      = 0.0;
y[1]      = 1.0;
hstart    = 0.0;
thresh[0] = 1.0e-8;
thresh[1] = 1.0e-8;
ruser[0]  = 1.0;
ruser[1]  = 1.0;

cout << "\n  Calculation with tol = " << tol << endl;
cout.setf(ios::fixed);
cout.setf(ios::right);

cout.precision(3);
cout << "\n    t         y1        y2" << endl;
cout.width(6);
cout << tstart;

for (int k = 0; k < n; k++)
{
cout.width(10);
cout << y[k];
}
cout << endl;

// Initialize Runge-Kutta method for integrating ODE
Integer ifail     = 0;
void *  ad_handle = 0;
nag::ad::d02pq(ad_handle, n, tstart, tend, y, tol, thresh, method, hstart,
iwsav, rwsav, ifail);

double tnow;
tnow = tstart;
while (tnow < tend)
{
ifail = 0;
nag::ad::d02pf(ad_handle, f, n, tnow, ynow, ypnow, -1, iuser, -1, ruser,
iwsav, rwsav, ifail);
cout.width(6);
cout << tnow;
for (int k = 0; k < n; ++k)
{
cout.width(10);
cout << ynow[k];
}
cout << endl;
}

double  hnext, waste;
Integer fevals, stepcost, stepsok;
ifail = 0;
nag::ad::d02pt(ad_handle, fevals, stepcost, waste, stepsok, hnext, iwsav,
rwsav, ifail);
cout << "\n Cost of the integration in evaluations of f is " << fevals;
cout << endl;

delete[] thresh;
delete[] ynow;
delete[] y;
delete[] ypnow;
delete[] iwsav;
delete[] rwsav;
return exit_status;
}

static void NAG_CALL f(void *&        ad_handle,
const double & t,
const Integer &n,
const double   y[],
double         yp[],
Integer        iuser[],
double         ruser[])
{
yp[0] = ruser[0] * y[1];
yp[1] = -ruser[1] * y[0];
}
```