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Spectral semi-discretisations of weakly nonlinear wave equations over long times

Authors
Lubich, Christian
Published in Foundations of Computational Mathematics. 2008, vol. 8, no. 3, p. 319-334
Abstract The long-time behaviour of spectral semi-discretisations of weakly nonlinear wave equations is analysed. It is shown that the harmonic actions are approximately conserved also for the semi-discretised system. 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.
Keywords Nonlinear wave equationSpectral semi-discretisationLong-time behaviour
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HAIRER, Ernst, LUBICH, Christian. Spectral semi-discretisations of weakly nonlinear wave equations over long times. In: Foundations of Computational Mathematics, 2008, vol. 8, n° 3, p. 319-334. https://archive-ouverte.unige.ch/unige:5203

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Deposited on : 2010-02-16

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