Solving Korteweg-De Vries and Forced Vander Pol-duffing Oscillator Equations Using Natural Decomposition Method.

Abstract

The Natural decomposition method is combination of Natural transform and Ado mian polynomial.This method was used to obtain the approximate analytical solutions of nonlinear differential equations. In particular, third order KdV equation and Forced Van der Pol-Duffing oscillator equation are considered. Adomian polynomial was intro duce as essential tool to linearize the associated nonlinear terms in the equations since Natural transform cannot handle nonlinear terms. All the problems considered show that the Natural decomposition method is very powerful integral transform methods in solving nonlinear equations like KDV equations. In addition we obtain the numeri cal solution of KDV equation using finite difference method and for Forced Van der Pol-Duffing oscillator equation we use RK4 method. Then we compare the numerical solution with the approximated analytic solution of this DEs. The finite difference and RK4 method of these DEs implemented in Matlab.