Abstract
In this article, the homotopy analysis method (HAM) for obtaining the analytical solution of the inverse parabolic problem and computing the unknown time-dependent parameter is introduced. The series solution is developed and the recurrence relations are given explicitly. Special attention is given to satisfy the convergence of the proposed method. A comparison of HAM with the variational iteration method is made. In the HAM, we use the auxiliary parameter h to control with a simple way in the convergence region of the solution series. Applying this method with several examples is presented to show the accuracy, simplicity and efficiency of the proposed approach.