Geometric Properties of Runge-Kutta Discretizations for Nonautonomous Index 2 Differential Algebraic Systems

J. Schropp

Mathematical and Computer Modelling of Dynamical Systems, 2001, vol. 7, issue 2, 263-271

Abstract: We analyze Runge-Kutta discretizations applied to nonautonomous index 2 differential algebraic equations (DAEs) in semi-explicit form. It is shown that for half-explicit and projected Runge-Kutta methods there is an attractive invariant manifold for the discrete system which is close to the invariant manifold of the DAE. The proof combines reduction techniques to autonomou index 2 differential algebraic equations with some invariant manifold results of Schropp [9]. The results support the favourable behavior of these Runge-Kutta methods applied to index 2 DAEs for t = 0.

Date: 2001
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DOI: 10.1076/mcmd.7.2.263.3653

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