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Numerical energy conservation for multi-frequency oscillatory differential equations

Lubich, Christian
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 methodsStörmer-Verlet methodHamiltonian systemsModulated Fourier expansionEnergy conservationOscillatory solutions
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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. doi: 10.1007/s10543-005-7121-z https://archive-ouverte.unige.ch/unige:12119

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Deposited on : 2010-10-15

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