caa a22 4500 605496889 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10543-014-0527-8 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0527-8 Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions [Elektronische Daten] [David Cohen, Ludwig Gauckler, Ernst Hairer, Christian Lubich] 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. Springer Science+Business Media Dordrecht, 2014 Oscillatory Hamiltonian systems nationallicence Modulated Fourier expansions nationallicence Trigonometric integrators nationallicence Störmer-Verlet scheme nationallicence IMEX scheme nationallicence Long-time energy conservation nationallicence Numerical resonances nationallicence Non-resonance condition nationallicence Cohen David Matematik och matematisk statistik, Umeå universitet, 90187, Umeå, Sweden aut Gauckler Ludwig Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany aut Hairer Ernst Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Geneva 4, Switzerland aut Lubich Christian Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, 72076, Tübingen, Germany aut BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 705-732 0006-3835 55:3<705 2015 55 10543 https://doi.org/10.1007/s10543-014-0527-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0527-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cohen David Matematik och matematisk statistik, Umeå universitet, 90187, Umeå, Sweden aut NATIONALLICENCE 700 1- Gauckler Ludwig Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany aut NATIONALLICENCE 700 1- Hairer Ernst Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Geneva 4, Switzerland aut NATIONALLICENCE 700 1- Lubich Christian Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, 72076, Tübingen, Germany aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 705-732 0006-3835 55:3<705 2015 55 10543