Mohsen Jalalian , Manochehr Kazemi , Mohammad Esmael Samei
{"title":"Solving the second kind Volterra-Fredholm type of two-dimensional integral equations on non-rectangular domains via radial basis functions","authors":"Mohsen Jalalian , Manochehr Kazemi , Mohammad Esmael Samei","doi":"10.1016/j.camwa.2025.07.027","DOIUrl":null,"url":null,"abstract":"<div><div>This research, introduces a method to solve two-dimensional nonlinear Volterra-Fredholm integral equations with non-rectangular domains, numerically, based on radial basis functions. The method doesn't need a background mesh or cell structure in the domain. In the approach, all of the integrals are estimated using Gauss-Legendre quadrature formula. Error analysis and the rate of convergence of this method are also investigated. Numerical examples are included to demonstrate the validity and efficiency of this method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 265-279"},"PeriodicalIF":2.5000,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0898122125003153","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
This research, introduces a method to solve two-dimensional nonlinear Volterra-Fredholm integral equations with non-rectangular domains, numerically, based on radial basis functions. The method doesn't need a background mesh or cell structure in the domain. In the approach, all of the integrals are estimated using Gauss-Legendre quadrature formula. Error analysis and the rate of convergence of this method are also investigated. Numerical examples are included to demonstrate the validity and efficiency of this method.
期刊介绍:
Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).