Re: ODE example

[Brian Gough <bjg at network-theory dot co dot uk>]

Slaven Peles writes:
 > Hi folks,
 > 
 > Could anybody send me a simple example of an ODE solver which uses a fixed 
 > step integrator? My C programing skills apparently are not good enough for me 
 > to figure it out myself from brief documentation and source codes that are 
 > available. I hope I would be able to learn it by example.
 > 
 > Many thanks,
 > Slaven 


Here's a variation on the example in the ode chapter,


#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_odeiv.h>

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

int
jac (double t, const double y[], double *dfdy, 
     double dfdt[], void *params)
{
  double mu = *(double *)params;
  gsl_matrix_view dfdy_mat 
    = gsl_matrix_view_array (dfdy, 2, 2);
  gsl_matrix * m = &dfdy_mat.matrix; 
  gsl_matrix_set (m, 0, 0, 0.0);
  gsl_matrix_set (m, 0, 1, 1.0);
  gsl_matrix_set (m, 1, 0, -2.0*mu*y[0]*y[1] - 1.0);
  gsl_matrix_set (m, 1, 1, -mu*(y[0]*y[0] - 1.0));
  dfdt[0] = 0.0;
  dfdt[1] = 0.0;
  return GSL_SUCCESS;
}

int
main (void)
{
  const gsl_odeiv_step_type * T 
    = gsl_odeiv_step_rk8pd;

  gsl_odeiv_step * s 
    = gsl_odeiv_step_alloc (T, 2);

  double mu = 10;
  gsl_odeiv_system sys = {func, jac, 2, &mu};

  double t = 0.0, t1 = 100.0;
  double h = 1e-2;
  double y[2] = { 1.0, 0.0 }, y_err[2], dfdy[4], dydt_in[2], dydt_out[2];

  /* initialise dydt_in */
  GSL_ODEIV_JA_EVAL(&sys, t, y, dfdy, dydt_in);

  while (t < t1)
    {
      int status = gsl_odeiv_step_apply (s, t, h, y, y_err, 
                                         dydt_in, dydt_out, &sys);

      if (status != GSL_SUCCESS)
          break;

      dydt_in[0] = dydt_out[0];
      dydt_in[1] = dydt_out[1];

      t += h;

      printf("%.5e %.5e %.5e\n", t, y[0], y[1]);
    }

  gsl_odeiv_step_free(s);
  return 0;
}