English

Uniform accuracy of implicit-explicit Runge-Kutta methods for linear hyperbolic relaxation systems

Numerical Analysis 2025-06-27 v2 Numerical Analysis Computational Physics

Abstract

In this paper, we study the uniform accuracy of implicit-explicit (IMEX) Runge-Kutta (RK) schemes for general linear hyperbolic relaxation systems satisfying the structural stability condition proposed in \cite{yong_singular_1999}. We establish the uniform stability and accuracy of a class of IMEX-RK schemes with spatial discretization using a Fourier spectral method. Our results demonstrate that the accuracy of the fully discretized schemes is independent of the relaxation time across all regimes. Numerical experiments on applications in traffic flows and kinetic theory verify our theoretical analysis.

Keywords

Cite

@article{arxiv.2410.07254,
  title  = {Uniform accuracy of implicit-explicit Runge-Kutta methods for linear hyperbolic relaxation systems},
  author = {Zhiting Ma and Juntao Huang},
  journal= {arXiv preprint arXiv:2410.07254},
  year   = {2025}
}

Comments

to be published in Journal of Scientific Computing. arXiv admin note: text overlap with arXiv:2306.08742 by other authors

R2 v1 2026-06-28T19:15:02.369Z