A quasi-reversibility regularization method for the Cauchy problem of the Helmholtz equation

被引：67

作者：

Zhang, H. W. ^{[1
,2
]}

Qin, H. H. ^{[1
]}

Wei, T. ^{[1
]}

机构：

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

[2] Hexi Univ, Dept Math, Zhangye City, Gansu, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2011年 / 88卷 / 04期

关键词：

ill-posed problem; Cauchy problem; Helmholtz equation; quasi-reversibility regularization method; convergence estimates; LAPLACE EQUATION;

D O I：

10.1080/00207160.2010.482986

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a Cauchy problem for the Helmholtz equation is considered. It is known that such a problem is severely ill-posed, i.e. the solution does not depend continuously on the given Cauchy data. We propose a quasi-reversibility regularization method to solve it. Convergence estimates are established under two different a priori assumptions for an exact solution. Numerical results obtained by two different schemes show that our proposed methods work well.

引用

页码：839 / 850

页数：12

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