{"title":"基于迭代正则化方案的第一类Fredholm积分方程的配置方法","authors":"T. Bechouat","doi":"10.3846/mma.2023.16453","DOIUrl":null,"url":null,"abstract":"To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required assumptions is detailed. Finally, numerical experiments demonstrate the efficiency of this method.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"13 1","pages":"237-254"},"PeriodicalIF":1.6000,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A collocation method for Fredholm integral equations of the First kind via iterative Regularization Scheme\",\"authors\":\"T. Bechouat\",\"doi\":\"10.3846/mma.2023.16453\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required assumptions is detailed. Finally, numerical experiments demonstrate the efficiency of this method.\",\"PeriodicalId\":49861,\"journal\":{\"name\":\"Mathematical Modelling and Analysis\",\"volume\":\"13 1\",\"pages\":\"237-254\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2023-03-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modelling and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3846/mma.2023.16453\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3846/mma.2023.16453","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A collocation method for Fredholm integral equations of the First kind via iterative Regularization Scheme
To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required assumptions is detailed. Finally, numerical experiments demonstrate the efficiency of this method.
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