Title :

High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates

Author(s) :

Besse, Christophe [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Dujardin, Guillaume [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Lacroix-Violet, Ingrid [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

SIAM Journal on Numerical Analysis

Pages :

1387-1411

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2017

ISSN :

0036-1429

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

This article deals with the numerical integration in time of nonlinear Schrödinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown ...
Show more >This article deals with the numerical integration in time of nonlinear Schrödinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the rotation term disappears and they obtain as a result a nonautonomous nonlinear Schrödinger equation. They consider exponential integrators such as exponential Runge–Kutta methods and Lawson methods. They provide an analysis of the order of convergence and some preservation properties of these methods in a simplified setting and they supplement their results with numerical experiments with realistic physical parameters. Moreover, they compare these methods with the classical split-step methods applied to the same problem.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Simulation numérique avancée pour les condensats de Bose-Einstein : Modèles numériques déterministes et stochastiques, Calcul haute performance, Simulation d'expériences physiques
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL