一类中立型时滞抛物型微分方程的无网格有限点法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-05-13 DOI:10.1016/j.enganabound.2025.106276

Yanxia Zhang , Xiaolin Li

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引用次数: 0

摘要

本文提出了求解一类中立型时滞抛物型微分方程的无网格有限点法。利用差分技术和时间上的泰勒展开，建立了中立型时滞初边值问题的二阶精确时间半离散系统。然后，结合移动最小二乘逼近和空间配置技术，构造了一个完全离散的无网格FPM系统。从理论上对所提出的FPM求解中立型时滞抛物型问题的精度进行了分析。最后，通过数值实验验证了该方法的有效性和准确性。

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A meshless finite point method for a class of parabolic differential equation of neutral delay

In this paper, a meshless finite point method (FPM) is proposed to solve a class of parabolic differential equation of neutral delay. By using difference techniques and Taylor expansions in time, a second-order accurate time semi-discrete system is established for the neutral delay initial–boundary value problem. Then, by combining the moving least squares approximation and the collocation technique in space, a fully discrete meshless FPM system is constructed. The accuracy analysis of the proposed FPM for solving the neutral delay parabolic problem is discussed in theory. Finally, some numerical experiments are provided to verify the effectiveness and accuracy of the FPM.

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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.