The Possible Solutions for the two KdV-type Equations Using a Semi-analytical Kamal-iteration Method

Abstract

In this paper, we used a semi-analytical method that combines the Kamal transform and a modified iteration method to solve the nonlinear homogeneous and nonhomogeneous modified Kerteweg-de Vries and the fifth-order Kerteweg-de Vries equations. The modified iteration method has been used to with a condition that guarantees fast convergence of the approximate solution. The analysis and convergence of the combined method have been discussed. Furthermore, the numerical simulations are presented to illustrate the effectiveness of the proposed semi-analytical method.