This article investigates the nonlocal inverse boundary-value problem for a rectangular domain, second order, two-dimensional elliptic equation. The article's main objective is to find the unidentified coefficient and offer a solution to the problem. The second-order, two-dimensional convection equation is solved directly using (FDM) finite difference method. However, the inverse problem was successfully solved by the MATLAB subroutine lsqnonlin from the optimization toolbox after being reformulated as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Given that the studied problem is often ill-posed and that even a minor error in the input data can have a large impact on the output, Tikhonov's regularization technique is used to generate stable and regularized results.