Attracting sets in index 2 differential algebraic equations and in their Runge-Kutta discretizations

Authors:
Johannes Schropp
Affiliations:
Department of Mathematics and Statistics, University of Konstanz, P.O. Box 5560, Konstanz D-78434, Germany
Venue:
Nonlinear Analysis: Theory, Methods & Applications
Year:
2003

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Abstract

We analyse Runge-Kutta discretizations applied to autonomous index 2 differential algebraic equations in the vicinity of attracting sets. We compare the geometric properties of the numerical and the exact solutions and show that projected and half-explicit Runge-Kutta methods reproduce the qualitative features of the continuous system correctly. The proof combines invariant manifold results of Schropp (SIAM J. Numer. Anal., to appear) and classical results for discretized ordinary differential equations of Kloeden and Lorenz (SIAM J. Numer. Anal. 23 (1986) 986).