Numerical solution of Hamiltonian model by using homotopy analysis method

Abstract

In this paper, a Hamiltonian model is solved by using the Adomian's deomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variation alliteration method (MVIM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.