Extrapolation-Based Implicit-Explicit Peer Methods with Optimised Stability Regions
For computational scientists solving stiff ODEs, this provides new IMEX methods with improved stability, though the improvement is incremental over existing IMEX-Peer approaches.
The paper introduces a new class of implicit-explicit Peer methods for ODEs with stiff and non-stiff parts, using extrapolation to achieve optimized stability regions. Methods of orders 2, 3, and 4 are presented, with numerical experiments showing competitive performance.
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.