Solving a nonlinear inverse problem of identifying an unknown source term in a reaction-diffusion equation by adomian decomposition method

Abstract

We consider the inverse problem of finding the nonlinear source for nonlinear Reaction-Diffusion equation whenever the initial and boundary condition are given. We investigate the numerical solution of this problem by using Adomian Decomposition Method (ADM). The approach of the proposed method is to approximate unknown coefficients by a nonlinear function whose coefficients are determined from the solution of minimization problem based on the overspecified data. Further, the Tikhonov regularization method is applied to deal with noisy input data and obtain a stable approximate solution. This method is tested for two examples. The results obtained show that the method is efficient and accurate. This study showed also, the speed of the convergent of ADM.