{"title":"Modified regularization method for a Cauchy problem of the Laplace equation","authors":"Jian-feng Mao, Guangfu Wang","doi":"10.1109/ICIST.2011.5765204","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the Cauchy problem for the Laplace's equation in a rectangle, where the Cauchy data is given for y = 0 and boundary data are given for x = 0 and x = π. The solution is sought in the interval 0 < y ≤ 1. A modified method is presented and error estimate is obtained. Combining the method of modified, we implement the numerical solution. A numerical example shows that the method works well.","PeriodicalId":6408,"journal":{"name":"2009 International Conference on Environmental Science and Information Application Technology","volume":"17 1","pages":"27-32"},"PeriodicalIF":0.0000,"publicationDate":"2011-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Conference on Environmental Science and Information Application Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICIST.2011.5765204","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we consider the Cauchy problem for the Laplace's equation in a rectangle, where the Cauchy data is given for y = 0 and boundary data are given for x = 0 and x = π. The solution is sought in the interval 0 < y ≤ 1. A modified method is presented and error estimate is obtained. Combining the method of modified, we implement the numerical solution. A numerical example shows that the method works well.
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