IMEX peer methods for fast-wave–slow-wave problems

Abstract

Differential equations with both stiff and nonstiff parts can be solved efficiently by implicit–explicit (IMEX) methods. There have been considered various approaches in the literature. In this paper we introduce IMEX peer methods. We show that the combination of s-stage explicit and implicit peer methods, both of order p, gives an IMEX peer method of the same order. We construct methods of order p=s for s=3,4, where we compute the free parameters numerically to give good stability with respect to fast-wave–slow-wave problems from weather prediction. We implement these methods with and without step size control. Tests and comparisons with other methods for problems mostly from weather prediction show the high potential of IMEX peer methods.