Multirate methods for ordinary differential equations

This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system. We start the discussion with the straightforward approach based on interpolating and extrapolating the slow--fast coupling variables; the multirate Euler scheme, used as a base example, falls into this class. Next we discuss higher order multirate schemes that generalize classical singlerate linear multistep, Runge-Kutta, and extrapolation methods.