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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 @math{(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 is process is continued until an acceptable step-size is found.

Function: gsl_odeiv_evolve * gsl_odeiv_evolve_alloc (size_t dim)
This function returns a pointer to a newly allocated instance of an evolution function for a system of dim dimensions.

Function: int gsl_odeiv_evolve_apply (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[])
This function advances the system (e, dydt) from time t and position y using the stepping function step. The new time and position are stored in t and y on output. The initial step-size is taken as h, but this will be modified using the control function c to achieve the appropriate error bound if necessary. The routine may make several calls to step in order to determine the optimum step-size. If the step-size has been changed the value of h will be modified on output. The maximum time t1 is guaranteed not to be exceeded by the time-step. On the final time-step the value of t will be set to t1 exactly.

Function: int gsl_odeiv_evolve_reset (gsl_odeiv_evolve * e)
This function resets the evolution function e. It should be used whenever the next use of e will not be a continuation of a previous step.

Function: void gsl_odeiv_evolve_free (gsl_odeiv_evolve * e)
This function frees all the memory associated with the evolution function e.

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