Numerical solution of Boussinesq equation using modified Adomian decomposition and homotopy analysis methods

‎In this paper‎, ‎a Boussinesq equation is solved by using the‎ ‎Adomianʹs decomposition method‎, ‎modified Adomianʹs decomposition‎ ‎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 in detail‎. ‎A numerical example is‎ ‎studied to demonstrate the accuracy of the presented methods‎.