Numerical solution to inverse coefficient problem for hyperbolic equation under overspecified condition of general integral type

We investigate solving the inverse coefficient issue for a hyperbolic equation under overspecified condition of general integral type. Crank–Nicolson finite difference method (FDM) combined with the trapezoidal rule quadrature has been used for direct problem. While, the inverse problem was reformulated as nonlinear regularized least-square optimization problem with simple bound and solved efficiently by MATLAB subroutine lsqnonlin from optimization toolbox. Since problem under investigation is generally ill-posed, small error in the input data lead to huge error in the output, then Tikhonov's regularization technique is applied to obtain a regularized stable results.