Well-Balanced and Asymptotic Preserving IMEX-Peer Methods

TL;DR

This paper introduces IMEX-Peer methods that are inherently well-balanced and asymptotic preserving, making them suitable for hyperbolic balance law systems, with numerical results confirming their effectiveness.

Contribution

The paper demonstrates that IMEX-Peer methods naturally possess well-balanced and asymptotic preserving properties without extra constraints on coefficients.

Findings

Methods are well-balanced and asymptotic preserving by design.

Numerical examples confirm theoretical properties.

Potential applications in hyperbolic systems of balance laws.

Abstract

Peer methods are a comprehensive class of time integrators offering numerous degrees of freedom in their coefficient matrices that can be used to ensure advantageous properties, e.g. A-stability or super-convergence. In this paper, we show that implicit-explicit (IMEX) Peer methods are well-balanced and asymptotic preserving by construction without additional constraints on the coefficients. These properties are relevant when solving (the space discretisation of) hyperbolic systems of balance laws, for example. Numerical examples confirm the theoretical results and illustrate the potential of IMEX-Peer methods.