Numerical identification of timewise dependent coefficient in Hyperbolic inverse problem

This article investigates the nonlocal inverse initial boundary-value problem in a rectangular domain, hyperbolic second order inverseproblem. The main objective is to find the unidentified coefficient and offer a solution to the problem. The hyperbolic second-order, nonlinear equation is solved using finite difference method (FDM). 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 op-timization 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 andaccurate results