/*
 * The program solves the first-order nonlinear equation,
 *
 *   y'(t) = u(t)^2  - u(t)^3
 *
 *   y[0] = 0.0001, 0 <= t <= 20000
 */

#include <stdio.h>

#include <gsl/gsl_errno.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_odeiv2.h>

int func (double t, const double y[], double f[], void *params) {
  f[0] = y[0]*y[0]*(1. - y[0]);
  return GSL_SUCCESS;
}

int main (void) {
  size_t neqs = 1;                       /* number of equations */
  double eps_abs = 1.e-10, eps_rel = 0.; /* desired precision */
  double stepsize = 1e-6;                /* initial integration step size */
  double t = 0., t1 = 20000.;            /* time interval of the evolution */
  int status;
  /* 
   * Initial conditions 
   */
  double y[1] = { 0.0001 };

  /*
   * Explicit embedded Runge-Kutta-Fehlberg (4,5) method. 
   * This method is a good general-purpose integrator.
   */
  gsl_odeiv2_step    *s = gsl_odeiv2_step_alloc (gsl_odeiv2_step_rkf45, neqs);
  gsl_odeiv2_control *c = gsl_odeiv2_control_y_new (eps_abs, eps_rel);
  gsl_odeiv2_evolve  *e = gsl_odeiv2_evolve_alloc (neqs);

  gsl_odeiv2_system sys = {func, NULL, neqs, NULL};

  /*
   * Evolution loop 
   */
  while (t < t1) {
      status = gsl_odeiv2_evolve_apply (e, c, s, &sys, &t, t1, &stepsize, y);

      if (status != GSL_SUCCESS) {
          printf ("Troubles at % .5e % .5e \n", t, y[0]);
          break;
      }

      printf ("% .5e % .5e \n", t, y[0]);
  }

  gsl_odeiv2_evolve_free (e);
  gsl_odeiv2_control_free (c);
  gsl_odeiv2_step_free (s);

  return 0;
}