A better method to determine the stability region of an L-stable implicit-explicit Runge-Kutta scheme

TL;DR

This paper introduces an improved method for accurately determining the stability region of L-stable IMEX Runge-Kutta schemes, addressing inaccuracies of previous methods and aiding in scheme analysis.

Contribution

The paper presents a novel, reliable method for stability region determination of IMEX schemes, ensuring correct results where prior methods failed.

Findings

The new method always provides correct stability regions.

Previous methods sometimes produced incorrect results.

The approach enhances analysis accuracy for IMEX schemes.

Abstract

We propose a better method to determine the stability region of an L-stable implicit-explicit Runge-Kutta scheme. This method always provides the correct result, while other methods sometimes give wrong result. It is useful in the analysis for implicit-explicit Runge-Kutta schemes. Keywords: Stability region, Implicit-explicit (IMEX) scheme