The Inverse source problem with a variable source coefficient

Abstract

The current research investigates an inverse source problem with variable coefficients in a nonhomogeneous hyperbolic equation. This linear inverse force problem divides into a direct problem and an inverse problem. Although the solution's uniqueness is well established in the literature, the inverse problem remains ill-posed because small data changes can cause significant errors. To obtain stable numerical solutions, we use a finite difference method combined with zero-order Tikhonov regularization. We test different regularization parameter and to choose the optimal parameter based on the error norm. Numerical experiments demonstrate that our method produces accurate results with exact data and remains stable even when noise is present.