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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Qian, Ai-Lin^1,2  Xiong, Xiang-Tuan³  Wu, Yu-Jiang² 

[1] Xianning Univ, Dept Math & Stat, Xianning 437000, Hubei, Peoples R China

[2] Lanzhou Univ, Dept Math, Lanzhou 730000, Gansu, Peoples R China

[3] NW Normal Univ, Dept Math, Lanzhou 730000, Gansu, Peoples R China

关键词: Ill-posed;    Cauchy problem of Helmholtz equation;    Quasi-reversibility;    Regularization;   

DOI  :  10.1016/j.cam.2009.09.031

来源: Elsevier

【 摘 要 】

In this paper, we consider the Cauchy problem for the Helmholtz equation in a rectangle, where the Cauchy data is given for y = 0 and boundary data are for x = 0 and x = pi. The solution is sought in the interval 0 < y <= 1. A quasi-reversibility method is applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

【 授权许可】

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