Application of numerical iterative methods for solving Benjamin-Bona-Mahony equation

Document Type : Original Research (Full Papers)

Author

Department of Mathematics Islamic Azad University Qazvin Branch, Qazvin, Iran

Abstract

In this paper, a generalized Benjamin-Bona-Mahony equation ( BBM)
is solved by using the Adomian's decomposition method (ADM) ,
modified Adomian's decomposition method (MADM), variational
iteration method (VIM), modified variational iteration 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.The MVIM has been shown to solve effectively, easily and accurately
a large class of nonlinear problems with the approximations which
convergent are rapidly to exact solutions.

Keywords