On the numerical solution to space fractional differential equations using meshless finite differences

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-10-24 DOI:10.1016/j.cam.2024.116322

A. García , M. Negreanu , F. Ureña , A.M. Vargas

引用次数: 0

Abstract

We derive a discretization of the Caputo and Riemann–Liouville spatial derivatives by means of the meshless Generalized Finite Difference Method, which is based on moving least squares. The conditional convergence of the method is proved and several examples over one dimensional irregular meshes are given.

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利用无网格有限差分法数值求解空间分数微分方程

我们通过基于移动最小二乘法的无网格广义有限差分法，推导出了卡普托和黎曼-刘维尔空间导数的离散化方法。证明了该方法的条件收敛性，并给出了一维不规则网格上的几个实例。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.