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/* ode-initval/rk2.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Runge-Kutta 2(3), Euler-Cauchy */
/* Author: G. Jungman
*/
/* Reference: Abramowitz & Stegun, section 25.5. Runge-Kutta 2nd (25.5.7)
and 3rd (25.5.8) order methods */
#include <config.h>
#include <stdlib.h>
#include <string.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_odeiv.h>
#include "odeiv_util.h"
typedef struct
{
double *k1;
double *k2;
double *k3;
double *ytmp;
}
rk2_state_t;
static void *
rk2_alloc (size_t dim)
{
rk2_state_t *state = (rk2_state_t *) malloc (sizeof (rk2_state_t));
if (state == 0)
{
GSL_ERROR_NULL ("failed to allocate space for rk2_state", GSL_ENOMEM);
}
state->k1 = (double *) malloc (dim * sizeof (double));
if (state->k1 == 0)
{
free (state);
GSL_ERROR_NULL ("failed to allocate space for k1", GSL_ENOMEM);
}
state->k2 = (double *) malloc (dim * sizeof (double));
if (state->k2 == 0)
{
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k2", GSL_ENOMEM);
}
state->k3 = (double *) malloc (dim * sizeof (double));
if (state->k3 == 0)
{
free (state->k2);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k2", GSL_ENOMEM);
}
state->ytmp = (double *) malloc (dim * sizeof (double));
if (state->ytmp == 0)
{
free (state->k3);
free (state->k2);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k2", GSL_ENOMEM);
}
return state;
}
static int
rk2_apply (void *vstate,
size_t dim,
double t,
double h,
double y[],
double yerr[],
const double dydt_in[],
double dydt_out[],
const gsl_odeiv_system * sys)
{
rk2_state_t *state = (rk2_state_t *) vstate;
size_t i;
double *const k1 = state->k1;
double *const k2 = state->k2;
double *const k3 = state->k3;
double *const ytmp = state->ytmp;
/* k1 step */
/* k1 = f(t,y) */
if (dydt_in != NULL)
{
DBL_MEMCPY (k1, dydt_in, dim);
}
else
{
int s = GSL_ODEIV_FN_EVAL (sys, t, y, k1);
if (s != GSL_SUCCESS)
{
return s;
}
}
/* k2 step */
/* k2 = f(t + 0.5*h, y + 0.5*k1) */
for (i = 0; i < dim; i++)
{
ytmp[i] = y[i] + 0.5 * h * k1[i];
}
{
int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k2);
if (s != GSL_SUCCESS)
{
return s;
}
}
/* k3 step */
/* for 3rd order estimates, is used for error estimation
k3 = f(t + h, y - k1 + 2*k2) */
for (i = 0; i < dim; i++)
{
ytmp[i] = y[i] + h * (-k1[i] + 2.0 * k2[i]);
}
{
int s = GSL_ODEIV_FN_EVAL (sys, t + h, ytmp, k3);
if (s != GSL_SUCCESS)
{
return s;
}
}
/* final sum */
for (i = 0; i < dim; i++)
{
/* Save original values if derivative evaluation below fails */
ytmp[i] = y[i];
{
const double ksum3 = (k1[i] + 4.0 * k2[i] + k3[i]) / 6.0;
y[i] += h * ksum3;
}
}
/* Derivatives at output */
if (dydt_out != NULL)
{
int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);
if (s != GSL_SUCCESS)
{
/* Restore original values */
DBL_MEMCPY (y, ytmp, dim);
return s;
}
}
/* Error estimation */
for (i = 0; i < dim; i++)
{
const double ksum3 = (k1[i] + 4.0 * k2[i] + k3[i]) / 6.0;
yerr[i] = h * (k2[i] - ksum3);
}
return GSL_SUCCESS;
}
static int
rk2_reset (void *vstate, size_t dim)
{
rk2_state_t *state = (rk2_state_t *) vstate;
DBL_ZERO_MEMSET (state->k1, dim);
DBL_ZERO_MEMSET (state->k2, dim);
DBL_ZERO_MEMSET (state->k3, dim);
DBL_ZERO_MEMSET (state->ytmp, dim);
return GSL_SUCCESS;
}
static unsigned int
rk2_order (void *vstate)
{
rk2_state_t *state = (rk2_state_t *) vstate;
state = 0; /* prevent warnings about unused parameters */
return 2;
}
static void
rk2_free (void *vstate)
{
rk2_state_t *state = (rk2_state_t *) vstate;
free (state->k1);
free (state->k2);
free (state->k3);
free (state->ytmp);
free (state);
}
static const gsl_odeiv_step_type rk2_type = { "rk2", /* name */
1, /* can use dydt_in */
1, /* gives exact dydt_out */
&rk2_alloc,
&rk2_apply,
&rk2_reset,
&rk2_order,
&rk2_free
};
const gsl_odeiv_step_type *gsl_odeiv_step_rk2 = &rk2_type;
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