Abstract
In the present paper, an efficient modification the convergence parameter based on the Adomian Decomposition Method (ADM) is proposed and investigated for a class of nonlinear evolution equations; specifically, the Korteweg de Vries (KdV) equations. We show that the proposed analysis possesses increased accuracy when compared to the standard ADM. Moreover, the optimal value of such a convergence parameter is determined by minimizing the averaged residual error. For such a convergence parameter value, an approximate solution is found to be closer to the available exact solution than the corresponding approximate solution without a convergence parameter for the same number of solution components. The approach proposed may be readily extended to other nonlinear differential and integral equations.