Inhalt des Dokuments
Preprint 05-2007
A discrete Adomian decomposition method for the discrete nonlinear Schrödinger equation
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.