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<h3 class="section">25.4 Evolution</h3>
<p>The highest level of the system is the evolution function which combines
the results of a stepping function and control function to reliably
advance the solution forward over an interval (t_0, t_1). If the
control function signals that the step-size should be decreased the
evolution function backs out of the current step and tries the proposed
smaller step-size. This process is continued until an acceptable
step-size is found.
<div class="defun">
— Function: gsl_odeiv_evolve * <b>gsl_odeiv_evolve_alloc</b> (<var>size_t dim</var>)<var><a name="index-gsl_005fodeiv_005fevolve_005falloc-2072"></a></var><br>
<blockquote><p>This function returns a pointer to a newly allocated instance of an
evolution function for a system of <var>dim</var> dimensions.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_odeiv_evolve_apply</b> (<var>gsl_odeiv_evolve * e, gsl_odeiv_control * con, gsl_odeiv_step * step, const gsl_odeiv_system * dydt, double * t, double t1, double * h, double y</var>[])<var><a name="index-gsl_005fodeiv_005fevolve_005fapply-2073"></a></var><br>
<blockquote><p>This function advances the system (<var>e</var>, <var>dydt</var>) from time
<var>t</var> and position <var>y</var> using the stepping function <var>step</var>.
The new time and position are stored in <var>t</var> and <var>y</var> on output.
The initial step-size is taken as <var>h</var>, but this will be modified
using the control function <var>c</var> to achieve the appropriate error
bound if necessary. The routine may make several calls to <var>step</var> in
order to determine the optimum step-size. An estimate of
the local error for the step can be obtained from the components of the array <var>e</var><code>->yerr[]</code>.
If the step-size has been changed the value of <var>h</var> will be modified on output.
The maximum time <var>t1</var> is guaranteed not to be exceeded by the time-step. On the
final time-step the value of <var>t</var> will be set to <var>t1</var> exactly.
<p>If the user-supplied functions defined in the system <var>dydt</var> return a
status other than <code>GSL_SUCCESS</code> the step will be aborted. In this
case, <var>t</var> and <var>y</var> will be restored to their pre-step values
and the error code from the user-supplied function will be returned. To
distinguish between error codes from the user-supplied functions and
those from <code>gsl_odeiv_evolve_apply</code> itself, any user-defined return
values should be distinct from the standard GSL error codes.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_odeiv_evolve_reset</b> (<var>gsl_odeiv_evolve * e</var>)<var><a name="index-gsl_005fodeiv_005fevolve_005freset-2074"></a></var><br>
<blockquote><p>This function resets the evolution function <var>e</var>. It should be used
whenever the next use of <var>e</var> will not be a continuation of a
previous step.
</p></blockquote></div>
<div class="defun">
— Function: void <b>gsl_odeiv_evolve_free</b> (<var>gsl_odeiv_evolve * e</var>)<var><a name="index-gsl_005fodeiv_005fevolve_005ffree-2075"></a></var><br>
<blockquote><p>This function frees all the memory associated with the evolution function
<var>e</var>.
</p></blockquote></div>
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