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

被引：10
|
作者：
Zhang, Hongwu [1 ,2 ]
Wei, Ting [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[2] Hexi Univ, Dept Math, Zhangye City 734000, Gansu, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2012年 / 59卷 / 02期
关键词：
Ill-posed problem; Cauchy problem; Laplace equation; Regularization method; Convergence estimate; REGULARIZATION; APPROXIMATION;
D O I：
10.1007/s11075-011-9487-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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
收藏
页码：249 / 269
页数：21
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