Title :

Energy preserving methods for nonlinear Schrödinger equations

Author(s) :

Besse, Christophe [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Descombes, Stephane [Auteur]
Laboratoire Jean Alexandre Dieudonné [LJAD]
Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media [NACHOS]
Dujardin, Guillaume [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Systèmes de particules et systèmes dynamiques [Paradyse]
Lacroix-Violet, Ingrid [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

IMA Journal of Numerical Analysis

Pages :

618–653

Publisher :

Oxford University Press (OUP)

Publication date :

2021-01

ISSN :

0272-4979

English keyword(s) :

Nonlinear Schrödinger equation
Relaxation methods
Numerical methods
Gross-Pitaevskii equation

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Physique [physics]/Physique [physics]/Optique [physics.optics]
Physique [physics]/Physique Quantique [quant-ph]

English abstract : [en]

This paper is concerned with the numerical integration in time of nonlinear Schrödinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method ...
Show more >This paper is concerned with the numerical integration in time of nonlinear Schrödinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in [10] for the cubic nonlinear Schrödinger equation. This method is also an energy preserving method and numerical simulations have shown that its order is 2. In this paper we give a rigorous proof of the order of this relaxation method and propose a generalized version that allows to deal with general power law nonlinearites. Numerical simulations for different physical models show the efficiency of these methods.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL