Attracting sets in index 2 differential algebraic equations and in their Runge-Kutta discretizations
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)].
scientific article; zbMATH DE number 1880003