This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists) does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

In this paper we investigate an ill posed diffusion system with a non diagonal diffusion matrix. Based on the quasi-boundary value method, we regularize the problem, we prove that the approximate solutions depend continuously on the data and we establish some convergence results. Finally numerical results are presented to illustrate the accuracy and efficiency of the proposed method.