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