SOLVABILITY OF THE THIRD-ORDER KORTEWEG-DE VRIES (KDV) EQUATION BY VARIATIONAL ITERATION AND NEW ITERATIVE METHODS

Abstract

This paper examined the approximate solution of the third-order Kortewed-de Vries (KdV) equations is obtained by the Variational Iteration Method (VIM) developed by Ji-Huan He and the New Iterative Method (NIM) developed by Daftardar Gejji and Jafari. These methods provide the solution in the form of a convergent series.which illustrate the ability and the effectiveness of the methods, some examples were provided. The results showed that the methods are very simple, effective, powerful and can easily be applied to other linear and nonlinear PDEs.