{"title":"ANALYTICAL AND NUMERICAL DISCUSSION FOR THE PHASE-LAG VOLTERRA-FREDHOLM INTEGRAL EQUATION WITH SINGULAR KERNEL","authors":"Mohammed Abdel-Aty, Mohammed Abdou","doi":"10.11948/20220547","DOIUrl":null,"url":null,"abstract":"In this paper, we studied the existence and unique solution of the Volterra-Fredholm integral equation of the second kind (V-FIESK). The general singular kernel is considered to be in position with the Fredholm integral term. Singular kernel will tend to a logarithmic function under exceptional conditions and new discussions. The Volterra-Fredholm integral equation with the logarithmic form will be solved using Legendre polynomials, where the kernel of Volterra integral term is a positive continuous function in time. A system of infinite linear algebraic equations is obtained by solving the problem in series, where the convergence of this system is discussed. Finally, The error is calculated using Maple software after the numerical results have been acquired.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"33 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Analysis and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11948/20220547","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we studied the existence and unique solution of the Volterra-Fredholm integral equation of the second kind (V-FIESK). The general singular kernel is considered to be in position with the Fredholm integral term. Singular kernel will tend to a logarithmic function under exceptional conditions and new discussions. The Volterra-Fredholm integral equation with the logarithmic form will be solved using Legendre polynomials, where the kernel of Volterra integral term is a positive continuous function in time. A system of infinite linear algebraic equations is obtained by solving the problem in series, where the convergence of this system is discussed. Finally, The error is calculated using Maple software after the numerical results have been acquired.
期刊介绍：
The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
