Solution of Index 2 Implicit Differential-Algebraic Equations by Lobatto Runge-Kutta Methods

Author: Jay L.O.

Source: Bit Numerical Mathematics, Volume 43, Number 1, March 2003 , pp. 93-106(14)

Publisher: Springer

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Abstract:

We consider the numerical solution of systems of index 2 implicit differential-algebraic equations (DAEs) by a class of super partitioned additive Runge–Kutta (SPARK) methods. The families of Lobatto IIIA-B-C-C^*-D methods are included. We show super-convergence of optimal order 2s-2 for the s-stage Lobatto families provided the constraints are treated in a particular way which strongly relies on specific properties of the SPARK coefficients. Moreover, reversibility properties of the flow can still be preserved provided certain SPARK coefficients are symmetric.

Keywords: Differential-algebraic equations; index 2; Lobatto coefficients; mechanical systems; implicit Runge–Kutta methods

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA. email: ljay@math.uiowa.edu and na.ljay@na-net.ornl.gov

Publication date: 2003-03-01