An improved non-local boundary value problem method for a cauchy problem of the Laplace equation

被引：0

作者：

Hongwu Zhang

Ting Wei

机构：

[1] Lanzhou University,School of Mathematics and Statistics

[2] Hexi University,Department of Mathematics

来源：

Numerical Algorithms | 2012年 / 59卷

关键词：

Ill-posed problem; Cauchy problem; Laplace equation; Regularization method; Convergence estimate;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we propose an improved non-local boundary value problem method to solve a Cauchy problem for the Laplace equation. It is known that the Cauchy problem for the Laplace equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Convergence estimates for the regularized solutions are obtained under a-priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method.

引用

页码：249 / 269

页数：20

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