On the homotopy analysis method for the exact solutions of Helmholtz equation

In this paper, the exact solutions of Helmholtz equation are obtained by means of the homotopy analysis method (HAM). This analytical method is employed to give approximate analytical solutions of Helmholtz equation. The auxiliary parameter ℏ in the HAM solutions has provided a convenient way of controlling the convergence region of series solutions. It is also shown that the solutions which are obtained by the Adomian decomposition method (ADM) and variational iteration method (VIM) are special cases of the solution obtained by HAM.