An Iterative Regularization Method for a
Class of Inverse Boundary Value Problems of Elliptic Type

Fairouz Zouyed

Applied Math Lab, University Badji Mokhtar-Annaba, P.O.Box. 12, Annaba 23000,
Algeria
E-mail: fzouyed@gmail.com

Souheyla Debbouche

Department of Mathematics, University Larbi Ben M'hidi, Oum El Bouaghi, Algeria
E-mail: Souheyla.prof@gmail.com

Received October 15, 2018, revised November 16, 2018.

Abstract

This paper deals with the problem of determining an unknown source and
an unknown boundary condition $u (0) $ in a boundary value problem of elliptic type from extra measurements at internal points. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. For solving 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 regularization approximation is obtained. Moreover, the numerical results are presented to illustrate the
accuracy and effciency of this method.