Efficient Runge-Kutta integrators for index-2 differential algebraic equations

Butcher, J.; Chan, R.

doi:10.1090/S0025-5718-98-00953-3

Efficient Runge-Kutta integrators for index-2 differential algebraic equations
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by J. C. Butcher and R. P. K. Chan PDF

Math. Comp. 67 (1998), 1001-1021 Request permission

Abstract:

In seeking suitable Runge-Kutta methods for differential algebraic equations, we consider singly-implicit methods to which are appended diagonally-implicit stages. Methods of this type are either similar to those of Butcher and Cash or else allow for the importation of a final derivative from a previous step. For these two classes, with up to three additional diagonally-implicit stages, we derive methods that satisfy appropriate order conditions for index-2 DAEs.

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