LStableDirk2

Second order diagonally implicit Runge Kutta method (Dirk) with two stages.

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

where

The stability function for this method is:

The method is L-stable:

Notes

This method is derived in detail in Alexander (1977). This method is more expensive than Crank-Nicolson, but has the advantage of being L-stable (the same type of stability as the implicit Euler method) so may be more suitable for "stiff" problems.

Input Parameters

  • variablesA subset of the variables that this time integrator should be applied to

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

    Unit:(no unit assumed)

    Controllable:No

    Description:A subset of the variables that this time integrator should be applied to

Optional Parameters

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

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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    Controllable:No

    Description:Set the enabled status of the MooseObject.

Advanced Parameters

References

  1. R. Alexander. Diagonally implicit runge-kutta methods for stiff odes. SIAM J. Numer. Anal., 14(6):1006–1021, 1977.[BibTeX]