```/* D02PU_P0W_F C++ Header Example Program.
*
* Copyright 2020 Numerical Algorithms Group.
*
* Mark 27.1, 2020.
*/

#include <nag.h>
#include <math.h>
#include <stdio.h>
#include <iostream>
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 = 4;
const Integer     liwsav = 130;
const Integer     lrwsav = 350 + 32 * n;

Integer           exit_status = 0;

double            *rwsav = 0, *thresh = 0, *ygot = 0, *ymax = 0;
double            *ypgot = 0, *y = 0, ruser[1];
Integer           *iwsav = 0, iuser[1];
double            *rmserr = 0;

cout << "D02PU_P0W_F C++ Header Example Program Results\n\n";

thresh = new double [n];
ygot   = new double [n];
y      = new double [n];
ypgot  = new double [n];
ymax   = new double [n];
iwsav  = new Integer [liwsav];
rwsav  = new double [lrwsav];
rmserr = new double [n];

// Set initial conditions for ODE and parameters for the integrator.
Integer           method = 3;
double            tol, hstart, tend, tstart, eps;
eps    = 0.7;
tstart = 0.0;
tol    = 1.0e-6;
tend   = 3.0*nag_math_pi;
hstart = 0.0;
for (int i = 0; i < n; ++i) {
thresh[i] = 1.0e-10;
}

cout << "\n  Calculation with tol = " << tol << endl;

cout.setf(ios::fixed);
cout.setf(ios::right);
cout.precision(3);
cout << "\n    t         y1         y2         y3         y4" << endl;
cout.width(6); cout << tstart;

y[0] = 1.0 - eps;
y[1] = 0.0;
y[2] = 0.0;
y[3] = sqrt((1.0+eps)/(1.0-eps));
for (int k = 0; k < n; k++) {
cout.width(11); cout << y[k];
}
cout << endl;

// Initialize Runge-Kutta method for integrating ODE
Integer ifail = 0;
iwsav,rwsav,ifail);

double tgot, twant;
twant = tend;

ifail = 2;
while (ifail>1 && ifail<5) {
ifail = -1;
iwsav,rwsav,ifail);
}

if (ifail==0) {
cout.width(6); cout << tgot;
for (int k = 0; k < n; ++k) {
cout.width(11); cout << ygot[k];
}
cout << endl;

// Get Error estimates
double errmax, terrmx;
ifail = 0;

cout.setf(ios::scientific,ios::floatfield);
cout.precision(2);
cout << "\n Componentwise error assessment\n        ";
for (int k = 0; k < n; ++k) {
cout.width(11); cout << rmserr[k];
}
cout << endl;
cout.precision(3);
cout << "\n Worst global error observed was ";
cout.width(9); cout << errmax << endl;
cout << "              it occurred at T = ";
cout.width(8); cout << terrmx << endl;

double            hnext, waste;
Integer           fevals, stepcost, stepsok;
ifail = 0;
rwsav,ifail);
cout << "\n Cost of the integration in evaluations of f is " << fevals;
cout << endl;
}
delete [] thresh;
delete [] ygot;
delete [] y;
delete [] ypgot;
delete [] ymax;
delete [] iwsav;
delete [] rwsav;
delete [] rmserr;
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[])
{
double r;
r = 1.0/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;
}
```