New algorithm for the approximate solution of generalized seventh order Korteweg-Devries equation arising in shallow water waves

Abstract

In the present article, we present for the first time optimal auxiliary function method (OAFM) for partial differential equation (PDEs). To find efficient and precision the proposed method, we take Lax's seventh order korteweg-de Vries (KdV) and seventh order Sawada Kotera (SK) equations as test examples. The beauty of the planned method lies in auxiliary functions Ai and some parameters Ci which ensure a very rapid convergence of the solution. We compare the approximate solutions got by the proposed method with the homotopy perturbation method (HPM), the Optimal Homotopy asymptotic method. It should be emphasized that very good approximation is obtained at the first iteration. It has been shown, that OAFM is a simple and convergent method for the solution of nonlinear equations. The numerical results rendering that the applied method is explicit, efficacious and facile to utilize, for handling more general nonlinear equations.