Convergence of Iterative Methods applied to Boussinesq equation

In this paper, a Boussinesq equation is solved by using the Adomianʹs decomposition method, modified Adomianʹs decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. 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.