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Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
TU Berlin, Germany.
University of Geneva, Switzerland.
University of Tübingen, Germany.
2015 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 55, no 3, 705-732 p.Article in journal (Refereed) Published
Abstract [en]

For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time scales that cover arbitrary negative powers of the step size. This requires non-resonance conditions between the step size and the frequencies, but in contrast to previous results the results do not require any non-resonance conditions among the frequencies. The proof uses modulated Fourier expansions with appropriately modified frequencies.

Place, publisher, year, edition, pages
2015. Vol. 55, no 3, 705-732 p.
Keyword [en]
Oscillatory Hamiltonian systems, Modulated Fourier expansions, Trigonometric integrators, Störmer–Verlet scheme, IMEX scheme, Long-time energy conservation, Numerical resonances, Non-resonance condition
National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-99201DOI: 10.1007/s10543-014-0527-8ISI: 000361818100005OAI: diva2:786086
Available from: 2015-02-04 Created: 2015-02-04 Last updated: 2015-10-20Bibliographically approved

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