## SOLVING A NONLINEAR INVERSE PROBLEM OF IDENTIFYING AN UNKNOWN SOURCE TERM IN A REACTION-DIFFUSION EQUATION BY ADOMIAN DECOMPOSITION METHOD

SOLVING A NONLINEAR INVERSE PROBLEM OF IDENTIFYING AN UNKNOWN SOURCE TERM IN A REACTION DIFFUSION EQUATION BY ADOMIAN DECOMPOSITION METHOD

*REZA POURGHOLI, AKRAM SAEEDI*

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## Abstract

We consider the inverse problem of nding the nonlinear source for nonlin-

ear 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 co-

efficients by a nonlinear function whose coefficients are determined from the solution of

minimization problem based on the overspecied data. Further, the Tikhonov regular-

ization 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.

## Keywords

Inverse problem; Adomian Decomposition Method (ADM); Convergence; Overspecied data; Least Square; Tikhonov Regularization Method.