Approximate Solution of an Unknown Coefficients in Parabolic Equation

In this paper, an inverse parabolic equation is solved by using the homotopy analysis method (HAM) and the homotopy perturbation method (HPM). The approximation solution of this equation is calculated in the form of series which its components are computed easily. HPM is shown not always to generate a continuous family of solutions in terms of the homotopy parameter. By the convergence-control parameter this can however be prevented to occur in the HAM. Illustrative examples are presented to exhibit a comparison between the HAM and the HPM