Numerical Solutions Of Some Nonlinear Partial Differential Equations By The Decomposition Method***In this paper, the Adomian decomposition method (ADM) and the modified decomposition method (MDM) have been implemented for finding the solutions of Korteweg –de Vries and modified Korteweg –de Vries equations. The precision and speed of convergence of the numerical solution are verified through tables and illustrations via Mathematica software.