{"title":"用牛顿积积分法求解非线性奇异Volterra积分系统","authors":"B. Babayar-Razlighi , B. Soltanalizadeh","doi":"10.1016/j.mcm.2013.06.016","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider a nonlinear system of Volterra integral equations, and apply Newton’s method to linearize it. We solve each step of Newton’s system by the product integration technique. Also, we provide the sufficient conditions for convergence of the numerical method. Finally, we give a test problem to illustrate the applicability and accuracy of the presented method.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 11","pages":"Pages 1696-1703"},"PeriodicalIF":0.0000,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.016","citationCount":"12","resultStr":"{\"title\":\"Numerical solution of a nonlinear singular Volterra integral system by the Newton product integration method\",\"authors\":\"B. Babayar-Razlighi , B. Soltanalizadeh\",\"doi\":\"10.1016/j.mcm.2013.06.016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider a nonlinear system of Volterra integral equations, and apply Newton’s method to linearize it. We solve each step of Newton’s system by the product integration technique. Also, we provide the sufficient conditions for convergence of the numerical method. Finally, we give a test problem to illustrate the applicability and accuracy of the presented method.</p></div>\",\"PeriodicalId\":49872,\"journal\":{\"name\":\"Mathematical and Computer Modelling\",\"volume\":\"58 11\",\"pages\":\"Pages 1696-1703\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.016\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical and Computer Modelling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0895717713002409\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical and Computer Modelling","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0895717713002409","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Numerical solution of a nonlinear singular Volterra integral system by the Newton product integration method
In this paper, we consider a nonlinear system of Volterra integral equations, and apply Newton’s method to linearize it. We solve each step of Newton’s system by the product integration technique. Also, we provide the sufficient conditions for convergence of the numerical method. Finally, we give a test problem to illustrate the applicability and accuracy of the presented method.
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