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Modulated Fourier expansions of highly oscillatory differential equations
Section de Mathématiques, Université de Genève.ORCID iD: 0000-0001-6490-1957
Section de Mathématiques, Université de Genève.
Mathematisches Institut, Universität Tübingen.
2003 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 3, no 4, 327-345 p.Article in journal (Refereed) Published
Abstract [en]

Modulated Fourier expansions are developed as a tool for gaining insight into the long-time behavior of Hamiltonian systems with highly oscillatory solutions. Particle systems of Fermi-Pasta-Ulam type with light and heavy masses are considered as an example. It is shown that the harmonic energy of the highly oscillatory part is nearly conserved over times that are exponentially long in the high frequency. Unlike previous approaches to such problems, the technique used here does not employ nonlinear coordinate transforms and can therefore be extended to the analysis of numerical discrelizations.

Place, publisher, year, edition, pages
2003. Vol. 3, no 4, 327-345 p.
Keyword [en]
modulated Fourier expansion, multiple time scales, adiabatic invariants, highly oscillatory differential equations, exponentially small error estimates
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-59173DOI: 10.1007/s10208-002-0062-xISI: 000186321500001OAI: oai:DiVA.org:umu-59173DiVA: diva2:551358
Available from: 2012-09-11 Created: 2012-09-11 Last updated: 2017-12-07Bibliographically approved

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Cohen, David

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