Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions
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
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.
Oscillatory Hamiltonian systems, Modulated Fourier expansions, Trigonometric integrators, Störmer–Verlet scheme, IMEX scheme, Long-time energy conservation, Numerical resonances, Non-resonance condition
IdentifiersURN: urn:nbn:se:umu:diva-99201DOI: 10.1007/s10543-014-0527-8ISI: 000361818100005OAI: oai:DiVA.org:umu-99201DiVA: diva2:786086