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Journal of Applied Mathematics
Volume 2012, Article ID 390876, 9 pages
http://dx.doi.org/10.1155/2012/390876
Research Article

Numerical Solution of the Inverse Problem of Determining an Unknown Source Term in a Heat Equation

Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Received 8 March 2012; Accepted 7 May 2012

Academic Editor: Hui-Shen Shen

Copyright © 2012 Xiuming Li and Suping Qian. 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 investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method.