LStableDirk4

Fourth-order diagonally implicit Runge Kutta method (Dirk) with five stages.

This method can be expressed as a Runge-Kutta method with the following Butcher Tableau:

The stability function for this method is:

The method is L-stable:

Notes

The method was found in Skvortsov (2006) but it may not be the original source. There is also a 4th-order rule with 5 stages on page 107 of Hairer and Wanner (1999) but its coefficients have less favorable "amplification factors" than the present rule.

Input Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Set the enabled status of the MooseObject.

References

  1. E. Hairer and G. Wanner. Vol. 2: Stiff and Differential-Algebraic Problems : Solving Ordinary Differential Equations. Volume 2. Springer, Berlin, 1999.[BibTeX]
  2. L. M. Skvortsov. Diagonally implicit runge-kutta methods for stiff problems. Computational Mathematics and Mathematical Physics, 46(12):2110–2123, 2006.[BibTeX]