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.

翻译：本文研究了满足\cite{yong_singular_1999}所提出结构稳定性条件的一般线性双曲松弛系统中隐式-显式龙格-库塔格式的一致精度。我们建立了一类采用傅里叶谱方法进行空间离散的隐式-显式龙格-库塔格式的一致稳定性与精度理论。研究结果表明，完全离散格式的精度在所有参数区域内均与松弛时间无关。在交通流与动理学理论应用中的数值实验验证了我们的理论分析。