Copyright © 2013 Xiao-Xiao Li 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 quasireversibility 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.