A local meshless numerical scheme based on the radial point interpolation for the generalized time-fractional Allen–Cahn equation

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-02-01 DOI:10.1016/j.enganabound.2024.106058

Ali Habibirad , Yadollah Ordokhani , Omid Baghani , Hadis Azin

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引用次数: 0

Abstract

This research has been conducted to investigate a numerical solution for the Allen–Cahn equation featuring the generalized fractional time derivative. The finite difference method is employed to discretize the equation in the time variable. Subsequently, an error estimate is derived for the proposed method in

L_{p, μ, q}

space. Furthermore, a meshless technique based on radial point interpolation is used to discretize the problem in spatial variables. Through these procedures, the equation is transformed into a system of linear equations at each time step. The method’s effectiveness for solving this equation is demonstrated by three examples on both regular and irregular domains. These examples illustrate that the current method has a high level of accuracy and efficiency for solving the given problem.

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基于径向点插值的广义时间分数阶Allen-Cahn方程局部无网格数值格式

本文研究了具有广义分数阶时间导数的Allen-Cahn方程的数值解。采用有限差分法在时间变量上对方程进行离散化。在Lp，μ，q空间中给出了该方法的误差估计。在此基础上，采用基于径向点插值的无网格技术对空间变量进行离散化处理。通过这些步骤，方程在每个时间步被转换成一个线性方程组。通过在规则域和不规则域上的三个算例，证明了该方法求解该方程的有效性。这些例子表明，目前的方法在解决给定问题方面具有很高的准确性和效率。

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

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.