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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 3 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 "gsl__config.h"
- #include <stdlib.h>
- #include <string.h>
- #include "gsl_errno.h"
- #include "gsl_odeiv.h"
- #include "gsl_ode-initval__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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