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diff --git a/gsl-1.9/ode-initval/gear1.c b/gsl-1.9/ode-initval/gear1.c
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+/* ode-initval/gear1.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.
+ */
+
+/* Gear 1. This is the implicit Euler a.k.a backward Euler method. */
+
+/* Author: G. Jungman
+ */
+
+/* Error estimation by step doubling, see eg. Ascher, U.M., Petzold,
+ L.R., Computer methods for ordinary differential and
+ differential-algebraic equations, SIAM, Philadelphia, 1998.
+ The method is also described in eg. this reference.
+*/
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_odeiv.h>
+
+#include "odeiv_util.h"
+
+typedef struct
+{
+ double *k;
+ double *y0;
+ double *y0_orig;
+ double *y_onestep;
+}
+gear1_state_t;
+
+static void *
+gear1_alloc (size_t dim)
+{
+ gear1_state_t *state = (gear1_state_t *) malloc (sizeof (gear1_state_t));
+
+ if (state == 0)
+ {
+ GSL_ERROR_NULL ("failed to allocate space for gear1_state", GSL_ENOMEM);
+ }
+
+ state->k = (double *) malloc (dim * sizeof (double));
+
+ if (state->k == 0)
+ {
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for k", GSL_ENOMEM);
+ }
+
+ state->y0 = (double *) malloc (dim * sizeof (double));
+
+ if (state->y0 == 0)
+ {
+ free (state->k);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
+ }
+
+ state->y0_orig = (double *) malloc (dim * sizeof (double));
+
+ if (state->y0_orig == 0)
+ {
+ free (state->y0);
+ free (state->k);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
+ }
+
+ state->y_onestep = (double *) malloc (dim * sizeof (double));
+
+ if (state->y_onestep == 0)
+ {
+ free (state->y0_orig);
+ free (state->y0);
+ free (state->k);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);
+ }
+
+ return state;
+}
+
+static int
+gear1_step (double *y, gear1_state_t *state,
+ const double h, const double t,
+ const size_t dim, const gsl_odeiv_system *sys)
+{
+ /* Makes an implicit Euler advance with step size h.
+ y0 is the initial values of variables y.
+
+ The implicit matrix equations to solve are:
+
+ k = y0 + h * f(t + h, k)
+
+ y = y0 + h * f(t + h, k)
+ */
+
+ const int iter_steps = 3;
+ int nu;
+ size_t i;
+ double *y0 = state->y0;
+ double *k = state->k;
+
+ /* Iterative solution of k = y0 + h * f(t + h, k)
+
+ Note: This method does not check for convergence of the
+ iterative solution!
+ */
+
+ for (nu = 0; nu < iter_steps; nu++)
+ {
+ int s = GSL_ODEIV_FN_EVAL(sys, t + h, y, k);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+
+ for (i=0; i<dim; i++)
+ {
+ y[i] = y0[i] + h * k[i];
+ }
+ }
+
+ return GSL_SUCCESS;
+}
+
+static int
+gear1_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)
+{
+ gear1_state_t *state = (gear1_state_t *) vstate;
+
+ size_t i;
+
+ double *y0 = state->y0;
+ double *y0_orig = state->y0_orig;
+ double *y_onestep = state->y_onestep;
+
+ /* initialization */
+ DBL_MEMCPY(y0, y, dim);
+
+ /* Save initial values for possible failures */
+ DBL_MEMCPY (y0_orig, y, dim);
+
+ /* First traverse h with one step (save to y_onestep) */
+ DBL_MEMCPY (y_onestep, y, dim);
+
+ {
+ int s = gear1_step (y_onestep, state, h, t, dim, sys);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+
+ /* Then with two steps with half step length (save to y) */
+ {
+ int s = gear1_step (y, state, h / 2.0, t, dim, sys);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original y vector */
+ DBL_MEMCPY (y, y0_orig, dim);
+ return s;
+ }
+ }
+
+ DBL_MEMCPY (y0, y, dim);
+
+ {
+ int s = gear1_step (y, state, h / 2.0, t + h / 2.0, dim, sys);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original y vector */
+ DBL_MEMCPY (y, y0_orig, dim);
+ return s;
+ }
+ }
+
+ /* Cleanup update */
+
+ if (dydt_out != NULL)
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original y vector */
+ DBL_MEMCPY (y, y0_orig, dim);
+ return s;
+ }
+ }
+
+ /* Error estimation */
+
+ for (i = 0; i < dim; i++)
+ {
+ yerr[i] = 4.0 * (y[i] - y_onestep[i]);
+ }
+
+ return GSL_SUCCESS;
+}
+
+static int
+gear1_reset (void *vstate, size_t dim)
+{
+ gear1_state_t *state = (gear1_state_t *) vstate;
+
+ DBL_ZERO_MEMSET (state->y_onestep, dim);
+ DBL_ZERO_MEMSET (state->y0_orig, dim);
+ DBL_ZERO_MEMSET (state->y0, dim);
+ DBL_ZERO_MEMSET (state->k, dim);
+ return GSL_SUCCESS;
+}
+
+static unsigned int
+gear1_order (void *vstate)
+{
+ gear1_state_t *state = (gear1_state_t *) vstate;
+ state = 0; /* prevent warnings about unused parameters */
+ return 1;
+}
+
+static void
+gear1_free (void *vstate)
+{
+ gear1_state_t *state = (gear1_state_t *) vstate;
+ free (state->y_onestep);
+ free (state->y0_orig);
+ free (state->y0);
+ free (state->k);
+ free (state);
+}
+
+static const gsl_odeiv_step_type gear1_type = { "gear1", /* name */
+ 0, /* can use dydt_in? */
+ 1, /* gives exact dydt_out? */
+ &gear1_alloc,
+ &gear1_apply,
+ &gear1_reset,
+ &gear1_order,
+ &gear1_free
+};
+
+const gsl_odeiv_step_type *gsl_odeiv_step_gear1 = &gear1_type;
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