Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter $\varepsilon$. In this work, we prove rigorously the uniform stability and uniform accuracy of a class of IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The result we obtain is optimal in the sense that it holds regardless of the value of $\varepsilon$ and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.

翻译：隐式-显式龙格-库塔（IMEX-RK）格式是处理包含刚性部分和非刚性部分的多尺度方程的常用方法，其中刚性部分由小参数$\varepsilon$表征。本文针对一类具有刚性松弛的线性双曲系统，严格证明了IMEX-RK格式的一致稳定性和一致精度。所得结果具有最优性，即无论$\varepsilon$取值如何，精度阶数均与原格式的设计阶数相同，不存在阶数降低现象。