To solve ODEs with different time scales which are localized over the components, multirate time stepping is examined. In this paper we introduce a self-adjusting time stepping strategy, in which the step size for a particular component is determined by its own local temporal variation, instead of using a single step for the whole system. We primarily consider implicit time stepping methods, suitable for stiff or mildly stiff ODEs. Numerical results for our multirate strategy are presented for several test problems. Comparisons with the corresponding single-rate schemes show that substantial gains in computational work and CPU times can be obtained.

Multirate time stepping, local time stepping, ordinary differential equations
Initial value problems (msc 65L05), Multistep, Runge-Kutta and extrapolation methods (msc 65L06), Mesh generation and refinement (msc 65L50)
Energy (theme 4)
Springer
BIT : Numerical Mathematics
Multirate time stepping for PDE's
Multiscale Dynamics

Savcenco, V, Hundsdorfer, W, & Verwer, J.G. (2007). A multirate time stepping strategy for stiff ODEs. BIT : Numerical Mathematics, 47(1), 137–155.