A generalized finite difference approach and splitting technique for the Kuramoto–Tsuzuki equation in multi-dimensional applications

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-04-30 DOI:10.1016/j.enganabound.2025.106267

Maedeh Nemati , Mostafa Abbaszadeh , Mahmoud A. Zaky , Mehdi Dehghan

引用次数: 0

Abstract

This study investigates the numerical solution of the Kuramoto–Tsuzuki equation in one, two and three dimensions. To effectively handle the equation’s nonlinear component, we employ a splitting technique, while the linear component is addressed using the Crank–Nicolson method for temporal discretization. Spatial discretization is achieved through the generalized finite difference method with a convergence order of

O (h^{2})

. We analyze the stability and convergence properties of the proposed schemes and provide numerical results to validate the theoretical findings. Additionally, examples in one, two and three dimensions, including irregular regions for the 2D equation, are presented to demonstrate the applicability of the methods.

查看原文本刊更多论文

多维应用中Kuramoto-Tsuzuki方程的广义有限差分方法及分裂技术

本文研究了一、二、三维Kuramoto-Tsuzuki方程的数值解。为了有效地处理方程的非线性分量，我们采用了分裂技术，而线性分量则使用Crank-Nicolson方法进行时间离散化。通过收敛阶为O（h2）的广义有限差分法实现空间离散化。我们分析了所提格式的稳定性和收敛性，并给出了数值结果来验证理论结论。此外，给出了一维、二维和三维的例子，包括二维方程的不规则区域，以证明该方法的适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.