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

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• 作者：Schropp ; Johannes
• 关键词：Differential algebraic equations ; Attractive sets ; Invariant manifolds ; Runge&ndash ; Kutta methods
• 刊名：Nonlinear Analysis
• 出版年：2003
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：February, 2003
• 卷：52
• 期：4
• 页码：1185-1197
• 文件大小：141 K

摘要

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).