{"title":"用Haar小波法求解非线性Fredholm积分方程","authors":"Ü. Lepik, E. Tamme","doi":"10.3176/phys.math.2007.1.02","DOIUrl":null,"url":null,"abstract":"A numerical method for solving nonlinear Fredholm integral equations, based on the Haar wavelet approach, is presented. Its efficiency is tested by solving four examples for which the exact solution is known. This allows us to estimate the exactness of the obtained numerical results. High accuracy of the results even in the case of a small number of grid points is observed.","PeriodicalId":308961,"journal":{"name":"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"76","resultStr":"{\"title\":\"Solution of nonlinear Fredholm integral equations via the Haar wavelet method\",\"authors\":\"Ü. Lepik, E. Tamme\",\"doi\":\"10.3176/phys.math.2007.1.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A numerical method for solving nonlinear Fredholm integral equations, based on the Haar wavelet approach, is presented. Its efficiency is tested by solving four examples for which the exact solution is known. This allows us to estimate the exactness of the obtained numerical results. High accuracy of the results even in the case of a small number of grid points is observed.\",\"PeriodicalId\":308961,\"journal\":{\"name\":\"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics\",\"volume\":\"67 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"76\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3176/phys.math.2007.1.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3176/phys.math.2007.1.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Solution of nonlinear Fredholm integral equations via the Haar wavelet method
A numerical method for solving nonlinear Fredholm integral equations, based on the Haar wavelet approach, is presented. Its efficiency is tested by solving four examples for which the exact solution is known. This allows us to estimate the exactness of the obtained numerical results. High accuracy of the results even in the case of a small number of grid points is observed.
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