A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION

被引：15

作者：

Yang, Fan ^{[1
,2
]}

Fu, Chuli ^{[2
]}

Li, Xiaoxiao ^{[1
]}

机构：

[1] Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Peoples R China

[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2015年 / 35卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Cauchy problem for Laplace equation; ill-posed problem; a posteriori parameter choice; error estimate; HEAT-CONDUCTION PROBLEM; COMPUTATION; WAVELETS;

D O I：

10.1016/S0252-9602(15)30058-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.

引用

页码：1339 / 1348

页数：10

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