Application of homotopy perturbation and Adomian dec- omposition methods for solving an inverse heat problem

Abstract

In this paper, the homotopy perturbation method is proposed to solve an inverse problem of finding an unknown function in parabolic equation with overspecified data. Comparison is made between Adomian decomposition method and the proposed method. It is shown; Adomian decomposition method is equivalent to the homotopy perturbation method in the model problem. To show the efficiency of these methods, several test problems are presented for one-, two- and three-dimensional cases. Comparison of the applied methods with exact solutions reveals that both methods are tremendously effective.