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Preprint 05-2007

A discrete Adomian decomposition method for the discrete nonlinear Schrödinger equation

Source file is available as :   Portable Document Format (PDF)

Author(s) : Ioannis Th. Famelis , Matthias Ehrhardt , Athanassios Bratsos

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 05-2007

MSC 2000

65M12 Stability and convergence of numerical methods
35Q40 Equations from quantum mechanics

Abstract :
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.

Keywords : Adomian decomposition method, discrete nonlinear Schröding er equations, finite difference schemes, solitons, plane waves, Mathematica

Notes :
Proceedings of HERCMA 2007 - The 8th Hellenic European Research on Computer Mathematics & its Applications Conference, Athens, September, 20-22, 2007.

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