Uniform accuracy of implicit-explicit Runge-Kutta methods for linear hyperbolic relaxation systems
<|reference_start|>Uniform accuracy of implicit-explicit Runge-Kutta methods for linear hyperbolic relaxation systems: 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.<|reference_end|>
@article{ma2024uniform,
    title={Uniform accuracy of implicit-explicit Runge-Kutta methods for linear
  hyperbolic relaxation systems},
    author={Zhiting Ma, Juntao Huang},
    journal={arXiv preprint arXiv:2410.07254},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.07254},
    primaryClass={math.NA cs.NA physics.comp-ph}
}