{"title":"第二类Volterra积分方程的逐次逼近(Neumann级数)方法","authors":"Teshome Bayleyegn Matebie","doi":"10.11648/J.PAMJ.20160506.16","DOIUrl":null,"url":null,"abstract":"In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2016-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Method of Successive Approximations (Neumann’s Series) of Volterra Integral Equation of the Second Kind\",\"authors\":\"Teshome Bayleyegn Matebie\",\"doi\":\"10.11648/J.PAMJ.20160506.16\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.\",\"PeriodicalId\":46057,\"journal\":{\"name\":\"Italian Journal of Pure and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2016-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Italian Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11648/J.PAMJ.20160506.16\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Italian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11648/J.PAMJ.20160506.16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Method of Successive Approximations (Neumann’s Series) of Volterra Integral Equation of the Second Kind
In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.
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