文章基本信息

标题：Modified Tikhonov Method for Cauchy Problem of Elliptic Equation with Variable Coefficients
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作者：Hongwu Zhang
期刊名称：American Journal of Computational Mathematics
印刷版ISSN：2161-1203
电子版ISSN：2161-1211
出版年度：2014
卷号：04
期号：03
页码：213-222
DOI：10.4236/ajcm.2014.43018
语种：English
出版社：Scientific Research Publishing
摘要：A Cauchy problem for the elliptic equation with variable coefficients is considered. This problem is severely ill-posed. Then, we need use the regularization techniques to overcome its ill-posedness and get a stable numerical solution. In this paper, we use a modified Tikhonov regularization method to treat it. Under the a-priori bound assumptions for the exact solution, the convergence estimates of this method are established. Numerical results show that our method works well.
关键词：Ill-Posed Problem; Cauchy Problem; Elliptic Equation with Variable Coefficients; Tikhonov Regularization Method; Convergence Estimates