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unige:12119 
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Numerical energy conservation for multi-frequency oscillatory differential equations |
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| Published in | BIT Numerical Mathematics. 2005, vol. 45, no. 2, p. 287-305 | |
| Abstract | The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with highly oscillatory solutions is studied in this paper. The numerical methods considered are second-order symmetric trigonometric integrators and the Störmer-Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system. A brief discussion of conservation properties in the continuous problem is also included. | |
| Keywords | Gautschi-type numerical methods — Störmer-Verlet method — Hamiltonian systems — Modulated Fourier expansion — Energy conservation — Oscillatory solutions | |
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Article (Author postprint) (1.7 MB) - Free access Other version: http://www.springerlink.com/content/b823440537857125/ |
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| Citation (ISO format) | COHEN, David, HAIRER, Ernst, LUBICH, Christian. Numerical energy conservation for multi-frequency oscillatory differential equations. In: BIT Numerical Mathematics, 2005, vol. 45, n° 2, p. 287-305. https://archive-ouverte.unige.ch/unige:12119 |
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