  In this paper we investigate a new class of implicit-explicit (IMEX) 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 is applied to construct IMEX
methods with favourable stability properties. Optimised IMEX-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.

Numerical Analysis