Multirate time stepping is a numerical technique for efficiently solving large-scale ordinary differential equations (ODEs) with widely different time scales localized over the components. This technique enables one to use large time steps for slowly varying components, and small steps for rapidly varying ones. Multirate methods found in the literature are normally of low order, one or two. Focusing on stiff ODEs, in this paper we discuss multirate methods based on the higher-order, stiff Rosenbrock integrators. Special attention is paid to the treatment of the refinement interfaces with regard to the choice of the interpolant and the occurrence of order reduction. For stiff, linear systems containing a stiff source term, we propose modifications for the treatment of the source term which overcome order reduction originating from such terms and which we can implement in our multirate method.

Multirate time stepping, local time stepping, high-order Rosenbrock methods, ordinary differential equations"
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). Construction of high-order multirate Rosenbrock methods for stiff ODEs. Modelling, Analysis and Simulation [MAS]. CWI.