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Scientific Article
unige:5203 
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Spectral semi-discretisations of weakly nonlinear wave equations over long times |
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| 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 equation — Spectral semi-discretisation — Long-time behaviour | |
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Article (Accepted version) (165 Kb) - Free access Other version: http://www.springerlink.com/content/e697027u2552x70h/ |
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| Structures | ||
| Citation (ISO format) | 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. doi: 10.1007/s10208-007-9014-9 https://archive-ouverte.unige.ch/unige:5203 |
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