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Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations

Cohen, David ; Hairer, Ernst ; Lubich, Christian

In: Numerische Mathematik, 2008, vol. 110, no. 2, p. 113-143

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    Titre
    • Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
    Auteur
    • Cohen, David. Mathematisches Institut, University of Basel, 4051, Basel, Switzerland
    • Hairer, Ernst. Dept. de Mathématiques, University of Geneva, 1211, Geneva 4, Switzerland
    • Lubich, Christian. Mathematisches Institut, University of Tübingen, 72076, Tübingen, Germany
    Type de document
    • Postprint
    Classification
    • Informatique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:314758
    Summary
    For classes of symplectic and symmetric time-stepping methods— trigonometric integrators and the Störmer-Verlet or leapfrog method—applied to spectral semi-discretizations of semilinear wave equations in a weakly non-linear setting, it is shown that energy, momentum, and all harmonic actions are approximately preserved over long times. For the case of interest where the CFL number is not a small parameter, such results are outside the reach of standard backward error analysis. Here, they are instead obtained via a modulated Fourier expansion in time