{"title":"On the numerical solution to space fractional differential equations using meshless finite differences","authors":"A. García , M. Negreanu , F. Ureña , A.M. Vargas","doi":"10.1016/j.cam.2024.116322","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"457 ","pages":"Article 116322"},"PeriodicalIF":2.6000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724005703","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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