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Numerical energy conservation for multi-frequency oscillatory differential equations
Section de Mathématiques, Université de Genève.
Section de Mathématiques, Université de Genève.
Mathematisches Institut, Universität Tübingen.
2005 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 45, no 2, 287-305 p.Article in journal (Refereed) Published
Abstract [en]

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 symmetric trigonometric integrators and the Stormer-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.

Place, publisher, year, edition, pages
2005. Vol. 45, no 2, 287-305 p.
Keyword [en]
Gautschi-type numerical methods, Stormer-Verlet method, Hamiltonian systems, modulated Fourier expansion, energy conservation, oscillatory solutions
National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-59172DOI: 10.1007/s10543-005-7121-zISI: 000232663400004OAI: diva2:551365
Available from: 2012-09-11 Created: 2012-09-11 Last updated: 2012-10-22Bibliographically approved

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