Efficient Runge-Kutta integrators for index-2

differential algebraic equations

Authors:
J. C. Butcher and R. P. K. Chan

Journal:
Math. Comp. **67** (1998), 1001-1021

MSC (1991):
Primary 65L05, 65L06, 65L20

MathSciNet review:
1464142

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**J. C. Butcher**

Affiliation:
Department of Mathematics, The University of Auckland, Auckland, New Zealand

Email:
butcher@math.auckland.ac.nz

**R. P. K. Chan**

Affiliation:
Division of Science and Technology, Tamaki Campus, The University of Auckland, Auckland, New Zealand

Email:
chan@scitec.auckland.ac.nz

DOI:
https://doi.org/10.1090/S0025-5718-98-00953-3

Keywords:
Differential algebraic systems of index 2,
singly-implicit Runge-Kutta methods,
diagonal extensions,
Laguerre polynomials

Received by editor(s):
December 9, 1994

Received by editor(s) in revised form:
April 16, 1997

Additional Notes:
The first author’s work was supported by the New Zealand Foundation for Research, Science and Technology.

Article copyright:
© Copyright 1998
American Mathematical Society