:orphan:

.. ****************************************************************************
.. CUI
..
.. The Advanced Framework for Simulation, Integration, and Modeling (AFSIM)
..
.. The use, dissemination or disclosure of data in this file is subject to
.. limitation or restriction. See accompanying README and LICENSE for details.
.. ****************************************************************************

.. _orbital_integrator_models:

.. include:: orbital_integrator_models.txt

Orbital Integrator Types
========================

.. _orbital_integrator_models.dormand_prince_45:

Prince-Dormand 45
*****************

.. parsed-literal::

   integrator_ prince_dormand_45
      ... :ref:`Embedded Runge-Kutta commands<orbital_integrator_models.embedded_runge_kutta>` ...
   end_integrator

This integrator is the embedded Runge-Kutta scheme RK5(4)7S as described in:
A family of embedded Runge-Kutta formulae, J.R. Dormand and P.J. Prince, Journal of
Computational and Applied Mathematics, Vol. 6, no 1, 1980.

This integrator gives a 5th order solution with a 4th order error estimator.
This integrator uses adaptive timesteps to control the error in the computed
solution.

.. _orbital_integrator_models.dormand_prince_78:

Prince-Dormand 78
*****************

.. parsed-literal::

   integrator_ prince_dormand_78
      ... :ref:`Embedded Runge-Kutta commands<orbital_integrator_models.embedded_runge_kutta>` ...
   end_integrator

This integrator is the embedded Runge-Kutta scheme RK8(7)13M as described in:
High order embedded Runke-Kutta formulae, P.J. Prince and J.R. Dormand, Journal
of Computational and Applied Mathematics, Vol. 7, no 1, 1981.

This integrator gives an 8th order solution with a 7th order error estimator.
This integrator uses adaptive timesteps to control the error in the computed
solution.

.. _orbital_integrator_models.embedded_runge_kutta:

Embedded Runge-Kutta
********************

The following commands are common to every embedded Runge-Kutta integrator
available for the :model:`WSF_INTEGRATING_SPACE_MOVER`.

.. command:: tolerance <real-value>

   This gives the error tolerance for a single step of the integrator. The default
   value for the tolerance is 1.0e-10.

.. command:: max_adjustment_attempts <integer-value>

   The maximum number of timestep adjustments attempts that will be made. If a
   suitable timestep is not found, a warning will be printed and the simulation
   will continue, but the satisfaction of the user requested tolerance is no
   longer guaranteed. The default value for this is 50.

.. command:: max_step_size <real-value>

   The maximum timestep in seconds. If the integrator would adapt its step size
   to larger than this value, it will use this value for the step size instead.
   The default value for this is effectively infinite.

.. command:: min_step_size <real-value>

   The minimum allowable timestep in seconds. If the integrator would adapt its
   step size to smaller than this value, it will use this value for the step
   size instead. The default value for this is 0.

   .. note:: Setting a non-zero value for this may cause the computed solution to no longer satisfy the specified tolerance.

.. command:: initial_step_size <real-value>

   The size of the initial step size in seconds for the first integration
   attempt. The default step size for this parameter is 0.1.

.. command:: error_criterion <error-criterion-type>

   Set the criterion for assessing the error in a step. The possible values are
   L_infinity and L_2. Selecting L_infinity will require that the maximum
   magnitude of any component of the error in the solution be smaller than the
   specified tolerance. Selecting L_2 will require the square root of the sum of
   the squared errors be smaller than the tolerance. Further, this error is
   computed as relative to the difference in the state over the computed step.

   The default option is L_2.