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Mathematics of Computation

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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: 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

R. P. K. Chan
Affiliation: Division of Science and Technology, Tamaki Campus, The University of Auckland, Auckland, New Zealand

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