Attracting sets in index 2 differential algebraic equations and in their Runge-Kutta discretizations
type: Item
instance of: scholarly article
title: Attracting sets in index 2 differential algebraic equations and in their Runge-Kutta discretizations
zbMATH Open document ID: 1032.34003
DOI: 10.1016/S0362-546X(02)00159-1
author: Johannes Schropp
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: Author's bstract: 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 [the author, SIAM J. Numer. Anal. 40, 872-890 (2002; Zbl 1053.65062)] and classical results for discretized ordinary differential equations of [\textit{P. E. Kloeden} and \textit{J. Lorenz}, SIAM J. Numer. Anal. 23, 986-995 (1986; Zbl 0613.65083)].
reviewed by: Oscar Lopez-Pouso
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L80
zbMATH DE Number: 1880003
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: attractive sets
zbMATH Keywords: invariant manifolds
zbMATH Keywords: Runge-Kutta methods
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1880003