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25.4 Evolution

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.

— 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.

If the user-supplied functions defined in the system dydt return a status other than GSL_SUCCESS the step will be aborted. In this case, t and y 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 gsl_odeiv_evolve_apply itself, any user-defined return values should be distinct from the standard GSL error codes.

— 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.