| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Domaine : |
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| Titre : |
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Birkhoff normal form for splitting methods applied to semilinear Hamiltonian PDEs. Part II: Abstract splitting. |
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| Auteur(s) : |
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Erwan Faou 1, 2, Benoît Grebert ( ) 3, Eric Paturel 3 |
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| Laboratoire : |
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| Équipe de recherche : |
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Analyse numérique |
| Résumé : |
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We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a normal form result for the corresponding discrete flow under generic non resonance conditions on the frequencies of the linear operator and on the step size. This result implies the conservation of the regularity of the numerical solution associated with the splitting method over arbitrary long time, provided the initial data is small enough. This result holds for numerical schemes controlling the round-off error at each step to avoid possible high frequency energy drift. We apply this results to nonlinear Schrödinger equations as well as the nonlinear wave equation. } |
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Langue du texte
intégral : |
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Anglais |
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| Journal : |
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| Numerische Mathematik |
| Publisher |
Springer Verlag (Germany) |
| ISSN |
0029-599X (eISSN : 0945-3245) |
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| Audience : |
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internationale |
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| Date de publication : |
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2010 |
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| Volume : |
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114 |
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| Numéro : |
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3 |
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| Page, identifiant, ... : |
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459-490 |
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| Mots Clés : |
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Birkhoff normal form – splitting methods – long time analysis |
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| Classification : |
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65P10, 37M15 |
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| Projet ANR : |
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| Référence du projet |
ANR-06-BLAN-0063 |
| Année |
2006 |
| Acronyme du projet |
RESONANCES |
| Titre du projet |
PETITS DIVISE ET RESONANCES EN GEOMETRIE, EDP ET DYNAMIQUE |
| Intitulé |
Programme "blanc |
| Acronyme de l'appel |
BLANC |
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