Normal form and long time analysis of splitting schemes for the linear Schrödinger equation.

Erwan Faou 1, 2 Guillaume Dujardin 1
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We consider the linear Schrödinger equation on a one dimensional torus and its time-discretization by splitting methods. Assuming a non-resonance condition on the stepsize and a small size of the potential, we show that the numerical dynamics can be reduced over exponentially long time to a collection of two dimensional symplectic systems for asymptotically large modes. For the numerical solution, this implies the long time conservation of the energies associated with the double eigenvalues of the free Schrödinger operator. The method is close to standard techniques used in finite dimensional perturbation theory, but extended here to infinite dimensional operators.
Type de document :
Rapport
[Research Report] RR-6015, INRIA. 2006, pp.41
Liste complète des métadonnées

https://hal.inria.fr/inria-00113480
Contributeur : Rapport de Recherche Inria <>
Soumis le : lundi 13 novembre 2006 - 17:54:52
Dernière modification le : vendredi 16 novembre 2018 - 01:31:28
Document(s) archivé(s) le : lundi 27 juin 2011 - 15:32:37

Fichiers

Identifiants

  • HAL Id : inria-00113480, version 2

Citation

Erwan Faou, Guillaume Dujardin. Normal form and long time analysis of splitting schemes for the linear Schrödinger equation.. [Research Report] RR-6015, INRIA. 2006, pp.41. 〈inria-00113480v2〉

Partager

Métriques

Consultations de la notice

439

Téléchargements de fichiers

127