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

页码：249 / 269

页数：21

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