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Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times

Hairer, E. ; Lubich, C.

In: Foundations of Computational Mathematics, 2008, vol. 8, no. 3, p. 319-334

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    Titre
    • Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times
    Auteur
    • Hairer, E.. Departement de Mathématiques, Université de Genève, 2-4 rue du Lièvre, CP 64, 1211, Genève 4, Switzerland
    • Lubich, C.. Mathematisches Institut, Universität Tübingen, 72076, Tübingen, Germany
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Foundations of Computational Mathematics, 2008, vol. 8, no. 3, p. 319-334. Springer-Verlag
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:320616
    Summary
    The long-time behaviour of spectral semi-discretisations of weakly non-linear wave equations is analysed. It is shown that the harmonic actions are approximately conserved for the semi-discretised system as well. This permits to prove that the energy of the wave equation along the interpolated semi-discrete solution remains well conserved over long times and close to the Hamiltonian of the semi-discrete equation. Although the momentum is no longer an exact invariant of the semi-discretisation, it is shown to be approximately conserved. All these results are obtained with the technique of modulated Fourier expansions