Comparison of the asymptotic stability for multirate Rosenbrock methods

Systems of ordinary differential equations containing different time scales can be treated by multirate extensions of singlerate integration methods. Since the stability properties of a singlerate method are usually not carried over to the corresponding multirate method, it is necessary to investigate the asymptotic stability of multirate methods. We apply different linearly implicit Rosenbrock methods in a recursive multirate procedure. For the interpolation, continuous extension, Hermite interpolation and a special monotone Hermite interpolation are considered. We give stability regions and illustrate their importance for a two-component test problem.