A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations

We present a new discrete Adomian decomposition method to approximate the theoretical solution of discrete nonlinear Schrödinger equations. The method is examined for plane waves and for single soliton waves in case of continuous, semi-discrete and fully discrete Schrödinger equations. Several illustrative examples and Mathematica program codes are presented

A discrete Adomian decomposition method for the discrete nonlinear Schrödinger equation

In this work we want to describe a discrete version of the well-known Adomian decomposition method (ADM) applied to nonlinear Schrödinger equations. The ADM was introduced by Adomian in the early 1980s to solve nonlinear ordinary and partial differential equation. This method is an alternative to finite difference and finite element methods; it avoids linearization and yields an efficient numerical solution with high accuracy