A stable numerical investigation based on geometric greedy points for 2D time-fractional partial integro-differential equations with singular kernels

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2025-03-01 Epub Date: 2025-01-30 DOI:10.1016/j.enganabound.2025.106129

Mojtaba Fardi, Banafsheh Raeisi, Mohammadreza Ahmadi Darani

引用次数: 0

Abstract

This paper develops a stable numerical method based on RBFs to solve two-dimensional time-fractional partial integro-differential equations with singular kernels. The spatial discretization uses an RBF-generated Hermite finite difference approach, which applies a geometric greedy sparse approximation technique for node selection, ensuring accuracy and controlling consistency errors. The temporal direction is discretized using a nonuniform formulation to achieve faster and more accurate temporal convergence compared to the uniform formulation. The method includes a detailed analysis of convergence and stability. Its accuracy and efficiency are tested with numerical examples, including cases with nonsmooth initial conditions, and compared to other existing methods, showing its superior performance.

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基于几何贪心点的二维奇异核时间分数阶偏积分微分方程的稳定数值研究

本文提出了一种基于rbf的二维奇异核时间分数型偏积分微分方程的稳定数值求解方法。空间离散化采用rbf生成的Hermite有限差分方法，该方法采用几何贪婪稀疏逼近技术进行节点选择，保证了精度并控制了一致性误差。采用非均匀公式对时间方向进行离散化，与均匀公式相比，可以实现更快、更精确的时间收敛。该方法对收敛性和稳定性进行了详细的分析。通过非光滑初始条件下的数值算例验证了该方法的精度和效率，并与其他现有方法进行了比较，显示了其优越的性能。

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.