An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

Abstract EN

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.