Identification of the unknown diffusion coefficient in a parabolic equation using HPM

Abstract

In this paper, the homotopy perturbation method (HPM) is proposed to solve an inverse problem of finding an unknown function in parabolic equation with an extra measurement. For solving the discussed inverse problem, at first we transform it\u2019s into a nonlinear direct problem then uses the proposed method. Also an error analysis is presented for the method and prior and posterior error bounds of the approximate solution are estimated. Application of the HPM to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution.