The homotopy analysis method for solving the Fornberg–Whitham equation and comparison with Adomian’s decomposition method

In this work, an analytical technique, namely the homotopy analysis method (HAM), is applied to obtain an approximate analytical solution of the Fornberg–Whitham equation. A comparison is made between the HAM results and the Adomian’s decomposition method (ADM) and the homotopy perturbation method (HPM). The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter ħħ, which provides us with a simple way to adjust and control the convergence region of solution series.