Stability analysis and error estimates of implicit-explicit Runge-Kutta least squares RBF-FD method for time-dependent parabolic equation

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2025-01-01 Epub Date: 2024-09-23 DOI:10.1016/j.apnum.2024.09.018

Huailing Song , Qingkui Tan

引用次数: 0

Abstract

In this paper, for the time-dependent parabolic equations defined on complex geometries domain, we develop and analyze the least-squares radial basis function finite difference method (RBF-FD) coupled with the implicit-explicit Runge-Kutta (IMEX-RK) time discretization up to third order accuracy, which improves stability and accuracy. We derive the absolute stability region and the optimal time-step constraint for four kinds of IMEX-RK schemes. Compared to the traditional explicit or implicit time discretization, these are not trivial. Under a wide time-step constraint, the stability and the error estimates in

l_{2}

-norm are established. Finally, several numerical experiments on the regular domain and non-convex domain are performed to validate the theoretical analysis.

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时变抛物方程的隐式-显式 Runge-Kutta 最小二乘 RBF-FD 方法的稳定性分析和误差估计

本文针对定义在复杂几何域上的时变抛物线方程，开发并分析了最小二乘径向基函数有限差分法（RBF-FD）与隐式-显式 Runge-Kutta （IMEX-RK）时间离散法（最高可达三阶精度），从而提高了稳定性和精度。我们推导了四种 IMEX-RK 方案的绝对稳定区域和最佳时间步长约束。与传统的显式或隐式时间离散化相比，这些并不简单。在宽时间步长约束下，建立了 l2 准则的稳定性和误差估计。最后，在规则域和非凸域上进行了若干数值实验，以验证理论分析。

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.