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Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions

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Abstract

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.

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Authors and Affiliations

  1. Matematik och matematisk statistik, Umeå universitet, 90187, Umeå, Sweden

    David Cohen

  2. Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Ludwig Gauckler

  3. Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Geneva 4, Switzerland

    Ernst Hairer

  4. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, 72076, Tübingen, Germany

    Christian Lubich

Authors
  1. David Cohen
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  2. Ludwig Gauckler
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  3. Ernst Hairer
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  4. Christian Lubich
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Corresponding author

Correspondence to Ludwig Gauckler.

Additional information

Communicated by Timo Eirola.

This work has been supported by the Fonds National Suisse, Project No. 200020-144313/1.

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Cohen, D., Gauckler, L., Hairer, E. et al. Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions. Bit Numer Math 55, 705–732 (2015). https://doi.org/10.1007/s10543-014-0527-8

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  • DOI: https://doi.org/10.1007/s10543-014-0527-8

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