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arXiv · 1402.4755

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

David Cohen·Ludwig Gauckler·Ernst Hairer·Christian Lubich
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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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David Cohen, Ludwig Gauckler, Ernst Hairer, Christian Lubich. 2014-02-19. Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions. https://arxiv.org/abs/1402.4755

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