This paper examines the finding of spacewise dependent heat source function in pseudoparabolic equation with initial and homogeneous Dirichlet boundary conditions, as well as the final time value / integral specification as additional conditions that ensure the uniqueness solvability of the inverse problem. However, the problem remains ill-posed because tiny perturbations in input data cause huge errors in outputs. Thus, we employ Tikhonov’s regularization method to restore this instability. In order to choose the best regularization parameter, we employ L-curve method. On the other hand, the direct (forward) problem is solved by a finite difference scheme while the inverse one is reformulated as an optimization problem. The

This paper presents a numerical solution to the inverse problem consisting of recovering time-dependent thermal conductivity and  heat source coefficients  in the one-dimensional  parabolic heat equation.   This  mathematical  formulation  ensures that the inverse problem  has a unique  solution.   However, the problem  is still  ill-posed since small errors  in the input data lead to a drastic  amount  of errors in the output coefficients.  The  finite  difference method  with  the Crank-Nicolson  scheme is adopted  as a direct  solver of the problem in a fixed domain.   The inverse problem is solved sub

     This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie