An accurate second-order ADI scheme for three-dimensional tempered evolution problems arising in heat conduction with memory

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-10 DOI:10.1016/j.apnum.2024.06.006

Mengmeng Liu , Tao Guo , Mahmoud A. Zaky , Ahmed S. Hendy

引用次数: 0

Abstract

An alternating direction implicit (ADI) scheme is proposed to study the numerical solution of a three-dimensional integrodifferential equation (IDE) with multi-term tempered singular kernels. Firstly, we employ the Crank-Nicolson method and the product integral (PI) rule on a uniform grid to approximate the temporal derivative and the multi-term tempered-type integral terms, thus establishing a second-order temporal discrete scheme. Then, a second-order finite difference method is used for spatial discretization and combined with the ADI technique to improve computational efficiency. Based on regularity conditions, the stability and convergence analysis of the ADI scheme is given by the energy argument. Finally, numerical examples confirm the results of the theoretical analysis and show that the method is effective.

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针对有记忆热传导中出现的三维钢化演化问题的精确二阶 ADI 方案

本文提出了一种交替方向隐式（ADI）方案，用于研究具有多期回火奇异内核的三维积分微分方程（IDE）的数值解法。首先，我们在均匀网格上采用 Crank-Nicolson 方法和积积分（PI）规则来逼近时域导数和多期回火型积分项，从而建立了一个二阶时域离散方案。然后，采用二阶有限差分法进行空间离散化，并结合 ADI 技术提高计算效率。基于正则条件，通过能量论证给出了 ADI 方案的稳定性和收敛性分析。最后，数值实例证实了理论分析的结果，并表明该方法是有效的。

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.