Solutions of time-dependent Emden–Fowler type equations by homotopy analysis method

In this Letter, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the time-dependent Emden–Fowler type equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown that the solutions obtained by the Adomian decomposition method (ADM) and the homotopy-perturbation method (HPM) are only special cases of the HAM solutions.