On the solution of a Korteweg-de Vries like equation by the decomposition method

Abstract

A new approach to a linear Korteweg-de Vries like equation is implemented by the Adomian decomposition method. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic [1-4]. It allows to obtain a decomposition series analytic solution of the equation which is calculated in the form of a convergent power series with easily computable components. The inhomogeneous problem is quickly solved by observing the self-canceling noise terms where the sum of components vanishes in the limit. Many test modeling problems from mathematical physics, linear and nonlinear, are discussed to illustrate the effectiveness and the performance of the decomposition method. This paper is particularly concerned with the accuracy for the modeling of various linear Korteweg-de Vries like equations by the Adomian decomposition method. Its remarkable accuracy is finally demonstrated in the study of several test problems.