dedalus.core.timesteppers
=========================

.. py:module:: dedalus.core.timesteppers

.. autoapi-nested-parse::

   ODE integrator classes for timestepping.





Module Contents
---------------

.. py:class:: CNAB1(solver)



   1st-order Crank-Nicolson Adams-Bashforth scheme [Wang 2008 eqn 2.5.3]

   Implicit: 2nd-order Crank-Nicolson
   Explicit: 1st-order Adams-Bashforth (forward Euler)



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 1



   .. py:attribute:: bmax
      :value: 1



   .. py:attribute:: cmax
      :value: 1



   .. py:attribute:: steps
      :value: 1



.. py:class:: CNAB2(solver)



   2nd-order Crank-Nicolson Adams-Bashforth scheme [Wang 2008 eqn 2.9]

   Implicit: 2nd-order Crank-Nicolson
   Explicit: 2nd-order Adams-Bashforth



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 2



   .. py:attribute:: bmax
      :value: 2



   .. py:attribute:: cmax
      :value: 2



   .. py:attribute:: steps
      :value: 2



.. py:class:: CNLF2(solver)



   2nd-order Crank-Nicolson leap-frog scheme [Wang 2008 eqn 2.11]

   Implicit: ?-order wide Crank-Nicolson
   Explicit: 2nd-order leap-frog



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 2



   .. py:attribute:: bmax
      :value: 2



   .. py:attribute:: cmax
      :value: 2



   .. py:attribute:: steps
      :value: 2



.. py:class:: MCNAB2(solver)



   2nd-order modified Crank-Nicolson Adams-Bashforth scheme [Wang 2008 eqn 2.10]

   Implicit: 2nd-order modified Crank-Nicolson
   Explicit: 2nd-order Adams-Bashforth



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 2



   .. py:attribute:: bmax
      :value: 2



   .. py:attribute:: cmax
      :value: 2



   .. py:attribute:: steps
      :value: 2



.. py:class:: RK111(solver)



   1st-order 1-stage DIRK+ERK scheme [Ascher 1997 sec 2.1]


   .. py:attribute:: A


   .. py:attribute:: H


   .. py:attribute:: c


   .. py:attribute:: stages
      :value: 1



.. py:class:: RK222(solver)



   2nd-order 2-stage DIRK+ERK scheme [Ascher 1997 sec 2.6]


   .. py:attribute:: A


   .. py:attribute:: H


   .. py:attribute:: c


   .. py:attribute:: stages
      :value: 2



   .. py:attribute:: γ


   .. py:attribute:: δ


.. py:class:: RK443(solver)



   3rd-order 4-stage DIRK+ERK scheme [Ascher 1997 sec 2.8]


   .. py:attribute:: A


   .. py:attribute:: H


   .. py:attribute:: c


   .. py:attribute:: stages
      :value: 4



.. py:class:: RKGFY(solver)



   2nd-order 2-stage scheme from Hollerbach and Marti


   .. py:attribute:: A


   .. py:attribute:: H


   .. py:attribute:: c


   .. py:attribute:: stages
      :value: 2



.. py:class:: RKSMR(solver)



   (3-ε)-order 3rd-stage DIRK+ERK scheme [Spalart 1991 Appendix]


   .. py:attribute:: A


   .. py:attribute:: H


   .. py:attribute:: c


   .. py:attribute:: stages
      :value: 3



.. py:class:: SBDF1(solver)



   1st-order semi-implicit BDF scheme [Wang 2008 eqn 2.6]

   Implicit: 1st-order BDF (backward Euler)
   Explicit: 1st-order extrapolation (forward Euler)



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 1



   .. py:attribute:: bmax
      :value: 1



   .. py:attribute:: cmax
      :value: 1



   .. py:attribute:: steps
      :value: 1



.. py:class:: SBDF2(solver)



   2nd-order semi-implicit BDF scheme [Wang 2008 eqn 2.8]

   Implicit: 2nd-order BDF
   Explicit: 2nd-order extrapolation



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 2



   .. py:attribute:: bmax
      :value: 2



   .. py:attribute:: cmax
      :value: 2



   .. py:attribute:: steps
      :value: 2



.. py:class:: SBDF3(solver)



   3rd-order semi-implicit BDF scheme [Wang 2008 eqn 2.14]

   Implicit: 3rd-order BDF
   Explicit: 3rd-order extrapolation



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 3



   .. py:attribute:: bmax
      :value: 3



   .. py:attribute:: cmax
      :value: 3



   .. py:attribute:: steps
      :value: 3



.. py:class:: SBDF4(solver)



   4th-order semi-implicit BDF scheme [Wang 2008 eqn 2.15]

   Implicit: 4th-order BDF
   Explicit: 4th-order extrapolation



   .. py:method:: compute_coefficients(timesteps, iteration)
      :classmethod:



   .. py:attribute:: amax
      :value: 4



   .. py:attribute:: bmax
      :value: 4



   .. py:attribute:: cmax
      :value: 4



   .. py:attribute:: steps
      :value: 4