Sayl Gani1,2, M. S. Hussein3
1 Department of Mathematics, College of Education for Pure Sciences Ibn Al-Haitham, University of Baghdad, Baghdad, Iraq.
2 Department of Computer Techniques Engineering, Imam Al-Kadhum College, Baghdad, Iraq.
3 Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.
This article investigates a nonlocal inverse initial boundary-value problem in a rectangular domain, formulated as a hyperbolic second-order inverse problem. The main objective is to identify the unknown coefficient and provide a stable solution. The nonlinear hyperbolic equation is solved using the finite difference method (FDM). The inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and solved using MATLAB’s lsqnonlin subroutine. Given that the studied problem is ill-posed and sensitive to input data, Tikhonov’s regularization technique is applied to ensure stability and accuracy in the numerical results.
Keywords: Finite difference method; Tikhonov regularization method; Hyperbolic inverse problem; Inverse problem.
Gani, S., & Hussein, M. S. (2023). Numerical identification of timewise dependent coefficient in hyperbolic inverse problem. Advances in the Theory of Nonlinear Analysis and Its Application, 7(4), 148–169.