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

TL;DR

This paper introduces a new class of implicit-explicit Peer methods for differential equations, using extrapolation to optimize stability regions and improve numerical performance.

Contribution

It develops and optimizes a novel extrapolation-based IMEX Peer method class with enhanced stability properties for stiff and non-stiff systems.

Findings

Optimized IMEX-Peer methods of orders 2, 3, 4 with large stability regions.

Numerical experiments demonstrate improved stability and efficiency.

Comparison shows advantages over existing IMEX methods.

Abstract

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.