Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times
نویسندگان
چکیده
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.
منابع مشابه
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ورودعنوان ژورنال:
- Foundations of Computational Mathematics
دوره 8 شماره
صفحات -
تاریخ انتشار 2008