#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "rk.h"

/*
  solve	\ddot{x} - 2 (1 - x^2) \dot{x} + x = 0
  
  canonical form
  \dot{x} = v
  \dot{v} = 2 (1 - x^2) v - x
*/

static void van_del_Pol(double t, int n, double q[], double dotq[])
{
  double x, v;
  
  x = q[0];
  v = q[1];
  
  dotq[0] = v;
  dotq[1] = 2 * (1 - x*x)*v - x;
}

#define	NumVars	2

main()
{
  double	dt = 0.001;
  const int	cnt = 10000;
  const double	tend = 10.00;
  
  double	t, q[NumVars];
  char		*filename = "van_der_Pol_rkf.dat";
  FILE		*fd;
  
  if ((fd = fopen(filename,"w")) == NULL) {
    fprintf(stderr, "cannot open %s\n", filename);
    exit(1);
  }
  
  /* initial values */
  t = 0.00;
  q[0] = 2.00;
  q[1] = 0.00;
  RKFadaptivefprint(fd, t, dt, NumVars, q);	// print initial values
  
  RKFadaptive(fd, &t, &dt, tend, cnt, NumVars, q, van_del_Pol);
  
  fclose(fd);
}