Identifying an Unknown Coefficient in the Reaction-Diffusion Equation Using He’s VIM

Abstract

An inverse heat problem of finding an unknown parameter p(t) in the parabolic initial-boundary value problem is solved with variational iteration method (VIM). For solving the discussed inverse problem, at first we transform it into a nonlinear direct problem and then use the proposed method. Also an error analysis is presented for the method and prior and posterior error bounds of the approximate solution are estimated. The main property of the method is in its flexibility and ability to solve nonlinear equation accurately and conveniently. Some examples are given to illustrate the effectiveness and convenience of the method.