Extrapolation-Based Implicit-Explicit Peer Methods with Optimised Stability Regions

In this paper we investigate an new class of implicit-explicit two-step methods of Peer type for systems of ordinary differential equations with both non-stiff and stiff parts included in the source term. An extrapolation approach based on already computed stage values with equally high consistency order is applied to construct such methods with strong stability properties. Optimised implicit-explicit Peer methods of order p=2,3,4, are given as result of a search algorithm carefully designed to balance the size of the stability regions and the extrapolation errors. Numerical experiments and a comparison to other implicit-explicit methods are included.