An Approximate Solution for a Second Order Elliptic Inverse Coefficient Problem with Nonlocal Integral

Authors

M. S. Hussein Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-9456-4303
Jehan A.Qahtan Ministry of Education, General Education in Baghdad-Rusafa II, Baghdad, Iraq https://orcid.org/0009-0001-2711-9824
Taysir E. Dyhoum The Department of Computing and Mathematics, Faculty of Science and Engineering, Manchester Metropolitan University, Manchester, UK https://orcid.org/0000-0002-1761-5904

DOI:

https://doi.org/10.30526/37.2.3477

Abstract

This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can have a large impact on the outcome, Tikhonov's regularization technique is used to obtain stable and regularized results.

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