Numerical analysis of nonlinear Klein–Gordon equations by a meshless superconvergent finite point method

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2024-09-17 DOI:10.1016/j.enganabound.2024.105954

Huanyang Hou, Xiaolin Li

引用次数: 0

Abstract

In this paper, we introduce a meshless method for numerical simulation of nonlinear Klein–Gordon equations. The method begins with a temporal discretization to address time derivatives. The stability and error of the temporal discretization scheme are theoretically analyzed. Subsequently, meshless algebraic systems of Klein–Gordon solitons are established by using the superconvergent finite point method (SFPM) for spatial discretization. The moving least squares approximation and its smoothed derivatives are adopted in the SFPM to ensure the high accuracy and remarkable superconvergence. Accuracy and convergence of the meshless numerical simulation for nonlinear Klein–Gordon equations are analyzed in theory. Numerical results validate the superconvergence and effectiveness of the method and confirm the theoretical analysis.

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用无网格超收敛有限点法对非线性克莱因-戈登方程进行数值分析

本文介绍了一种用于非线性克莱因-戈登方程数值模拟的无网格方法。该方法从时间离散化开始，以解决时间导数问题。从理论上分析了时间离散化方案的稳定性和误差。随后，利用超融合有限点法（SFPM）进行空间离散化，建立了克莱因-戈登孤子的无网格代数系统。SFPM 采用移动最小二乘近似及其平滑导数，以确保高精度和显著的超收敛性。理论分析了非线性克莱因-戈登方程无网格数值模拟的精度和收敛性。数值结果验证了该方法的超收敛性和有效性，并证实了理论分析。

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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.