ERK tableau registry
====================

.. currentmodule:: cubie.integrators.algorithms

``ERK_TABLEAU_REGISTRY`` maps human-friendly identifiers to
:class:`~cubie.integrators.algorithms.generic_erk.ERKTableau` instances. The
registry powers :func:`get_algorithm_step` aliases and allows callers to select
well-known explicit Runge--Kutta schemes without manually specifying the
coefficients.

.. autodata:: ERK_TABLEAU_REGISTRY
    :annotation: Dict[str, ERKTableau]

The default :class:`ERKStep` configuration uses
:data:`cubie.integrators.algorithms.generic_erk.DEFAULT_ERK_TABLEAU`, the
Dormand--Prince 5(4) pair. The ``"dopri54"`` alias mirrors the longer
``"dormand-prince-54"`` key so existing controller presets continue to work.

Available aliases
-----------------

.. list-table:: Named explicit Runge--Kutta tableaus
   :header-rows: 1

   * - Key
     - Description
     - Reference
   * - ``"heun-21"``
     - Heun's improved Euler method (order 2).
     - [Heun1900]_
   * - ``"ralston-33"``
     - Ralston's third-order method with minimized error constants.
     - [Ralston1962]_
   * - ``"bogacki-shampine-32"``
     - Bogacki--Shampine embedded 3(2) pair with FSAL property.
     - [BogackiShampine1993]_
   * - ``"dormand-prince-54"`` and ``"dopri54"``
     - Dormand--Prince embedded 5(4) pair with FSAL property.
     - [DormandPrince1980]_
   * - ``"classical-rk4"``
     - Classical fourth-order Runge--Kutta scheme.
     - [Kutta1901]_
   * - ``"cash-karp-54"``
     - Cash--Karp embedded 5(4) pair with adaptive control weights.
     - [CashKarp1990]_
   * - ``"fehlberg-45"``
     - Runge--Kutta--Fehlberg embedded 5(4) pair.
     - [Fehlberg1969]_

Tableau container
-----------------

.. autoclass:: cubie.integrators.algorithms.generic_erk_tableaus.ERKTableau
    :members:
    :show-inheritance:

References
----------

.. [Heun1900] K. Heun. *Neue Methoden zur approximativen Integration der
   Differentialgleichungen einer unabhängigen Veränderlichen.* Z. Math. Phys.
   45, 1900.
.. [Ralston1962] A. Ralston. "Runge-Kutta methods with minimum error bounds." *Math.
   Comp.* 16 (1962).
.. [BogackiShampine1993] P. Bogacki and L. F. Shampine. "An efficient Runge-Kutta (4,5)
   pair." *J. Comput. Appl. Math.* 46(1), 1993.
.. [DormandPrince1980] J. R. Dormand and P. J. Prince. "A family of embedded
   Runge-Kutta formulae." *J. Comput. Appl. Math.* 6(1), 1980.
.. [Kutta1901] W. Kutta. "Beitrag zur näherungsweisen Integration totaler
   Differentialgleichungen." *Zeitschr. Math. Phys.* 46, 1901.
.. [CashKarp1990] J. R. Cash and A. H. Karp. "A variable order Runge-Kutta method for
   initial value problems with rapidly varying right-hand sides." *ACM Trans.
   Math. Softw.* 16(3), 1990.
.. [Fehlberg1969] E. Fehlberg. *Low-order classical Runge-Kutta formulas with
   stepsize control and their application to some heat transfer problems.* NASA
   Technical Report 315, 1969.