Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 953492, 14 pages
http://dx.doi.org/10.1155/2011/953492
Research Article

The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

Fan Yang,1 HengZhen Guo,2 and XiaoXiao Li1

1School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2Institute of Education, Lanzhou City University, Lanzhou, Gansu 730070, China

Received 20 December 2010; Revised 6 April 2011; Accepted 25 April 2011

Academic Editor: Paulo Batista Gonçalves

Copyright © 2011 Fan Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the simplified Tikhonov regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.