The lowest level components are the stepping functions which advance a solution from time t to t+h for a fixed step-size h and estimate the resulting local error.
This function returns a pointer to a newly allocated instance of a stepping function of type T for a system of dim dimensions. Please note that if you use a stepper method that requires access to a driver object, it is advisable to use a driver allocation method, which automatically allocates a stepper, too.
This function resets the stepping function s. It should be used whenever the next use of s will not be a continuation of a previous step.
This function frees all the memory associated with the stepping function s.
This function returns a pointer to the name of the stepping function. For example,
printf ("step method is '%s'\n", gsl_odeiv2_step_name (s));
would print something like
step method is 'rkf45'.
This function returns the order of the stepping function on the previous step. The order can vary if the stepping function itself is adaptive.
This function sets a pointer of the driver object d for stepper s, to allow the stepper to access control (and evolve) object through the driver object. This is a requirement for some steppers, to get the desired error level for internal iteration of stepper. Allocation of a driver object calls this function automatically.
This function applies the stepping function s to the system of equations defined by sys, using the step-size h to advance the system from time t and state y to time t+h. The new state of the system is stored in y on output, with an estimate of the absolute error in each component stored in yerr. If the argument dydt_in is not null it should point an array containing the derivatives for the system at time t on input. This is optional as the derivatives will be computed internally if they are not provided, but allows the reuse of existing derivative information. On output the new derivatives of the system at time t+h will be stored in dydt_out if it is not null.
The stepping function returns
GSL_FAILURE if it is unable to
compute the requested step. Also, if the user-supplied functions
defined in the system sys return a status other than
GSL_SUCCESS the step will be aborted. In that case, the
elements of y will be restored to their pre-step values and the
error code from the user-supplied function will be returned. Failure
may be due to a singularity in the system or too large step-size
h. In that case the step should be attempted again with a
smaller step-size, e.g. h/2.
If the driver object is not appropriately set via
gsl_odeiv2_step_set_driver for those steppers that need it, the
stepping function returns
GSL_EFAULT. If the user-supplied
functions defined in the system sys returns
the function returns immediately with the same return code. In this
case the user must call
gsl_odeiv2_step_reset before calling
this function again.
The following algorithms are available,
Explicit embedded Runge-Kutta (2, 3) method.
Explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method. For more efficient estimate of the error, use the embedded methods described below.
Explicit embedded Runge-Kutta-Fehlberg (4, 5) method. This method is a good general-purpose integrator.
Explicit embedded Runge-Kutta Cash-Karp (4, 5) method.
Explicit embedded Runge-Kutta Prince-Dormand (8, 9) method.
Implicit Gaussian first order Runge-Kutta. Also known as implicit
Euler or backward Euler method. Error estimation is carried out by the
step doubling method. This algorithm requires the Jacobian and
access to the driver object via
Implicit Gaussian second order Runge-Kutta. Also known as implicit
mid-point rule. Error estimation is carried out by the step doubling
method. This stepper requires the Jacobian and access to the driver
Implicit Gaussian 4th order Runge-Kutta. Error estimation is carried
out by the step doubling method. This algorithm requires the Jacobian
and access to the driver object via
Implicit Bulirsch-Stoer method of Bader and Deuflhard. The method is generally suitable for stiff problems. This stepper requires the Jacobian.
A variable-coefficient linear multistep Adams method in Nordsieck
form. This stepper uses explicit Adams-Bashforth (predictor) and
implicit Adams-Moulton (corrector) methods in P(EC)^m
functional iteration mode. Method order varies dynamically between 1
and 12. This stepper requires the access to the driver object via
A variable-coefficient linear multistep backward differentiation
formula (BDF) method in Nordsieck form. This stepper uses the explicit
BDF formula as predictor and implicit BDF formula as corrector. A
modified Newton iteration method is used to solve the system of
non-linear equations. Method order varies dynamically between 1 and
5. The method is generally suitable for stiff problems. This stepper
requires the Jacobian and the access to the driver object via