An efficient modification of the decomposition method with a convergence parameter for solving Korteweg de Vries equations

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. (C) 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.