Three Semi-Analytical Methods for Ninth-Order Korteweg-de Vries Equation

Abstract

In this work, three powerful semi analytical methods, called Adomian decomposition method (ADM),Homotopy analysis method (HAM) and homotopy-perturbation method (HPM) are presented to obtain the series solutions of theninth-order Korteweg-de Vries(nKdV) equation for certain initial condition. The results obtained by these methods are then compared. The results show that these methods are very efficient and convenient and can be applied to a large class of problems. The numerical solutions are compared with the known analytical solutions.The comparison among these methods shows that although the numerical results of these methods are the same, because of the auxiliary parameter h and auxiliary H(x,t) function, HAM provides a better convergence than the other numerical methods.