Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2024-03-13 DOI:10.1090/mcom/3967

Jingwei Hu, Ruiwen Shu

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引用次数: 0

Abstract

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 ε \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 ε \varepsilon and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.

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含松弛双曲系统的隐式-显式 Runge-Kutta (IMEX-RK) 方案的均匀精度

隐式-显式 Runge-Kutta （IMEX-RK）方案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，其中刚性部分由一个小参数 ε \varepsilon 表征。在这项工作中，我们严格证明了一类 IMEX-RK 方案对具有刚性松弛的线性双曲系统的均匀稳定性和均匀精度。我们得到的结果是最优的，因为无论 ε \varepsilon 的值如何，它都是成立的，而且精度阶数与原始方案的设计阶数相同，即没有阶数降低。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.