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

✍ Scribed by Johannes Schropp

• Book ID: 104330415
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 141 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00159-1

✦ Synopsis

We analyse Runge-Kutta discretizations applied to autonomous index 2 di erential 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 di erential equations of Kloeden and Lorenz (SIAM J. Numer. Anal. 23 (1986) 986).