This paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use Rosenbrock type methods as the main time integration method and have one level of temporal local refinement. Some remarks on the relevance of the results for 2 x 2 test problems are presented.

Multirate time stepping, local time stepping, ordinary differential equations, asymptotic stability"
Initial value problems (msc 65L05), Multistep, Runge-Kutta and extrapolation methods (msc 65L06), Mesh generation and refinement (msc 65L50), Finite difference methods (msc 65M06), Method of lines (msc 65M20)
Energy (theme 4)
CWI
Modelling, Analysis and Simulation [MAS]
Multiscale Dynamics

Savcenco, V. (2007). Comparison of the asymptotic stability properties for two multirate strategies. Modelling, Analysis and Simulation [MAS]. CWI.