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High order numerical methods for highly oscillatory problem
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Karlsruhe Institute of Technology.
2015 (English)In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, Vol. 49, no 3, 695-711 p.Article in journal (Refereed) Published
Abstract [en]

This paper is concerned with the numerical solution of nonlinear Hamiltonian highly oscillatory systems of second-order differential equations of a special form. We present numerical methods of high asymptotic as well as time stepping order based on the modulated Fourier expansion of the exact solution. In particular we obtain time stepping orders higher than 2 with only a finite energy assumption on the initial values of the problem. In addition, the stepsize of these new numerical integrators is not restricted by the high frequency of the problem. Furthermore, numerical experiments on the modified Fermi–Pasta–Ulam problem as well as on a one dimensional model of a diatomic gas with short-range interaction forces support our investigations.

Place, publisher, year, edition, pages
2015. Vol. 49, no 3, 695-711 p.
Keyword [en]
Highly oscillatory differential equations, multiple time scales, Fermi–Pasta–Ulam problem, modulated Fourier expansions, high order numerical schemes, adiabatic invariants
National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-99203DOI: 10.1051/m2an/2014056ISI: 000354794100004OAI: diva2:786087
Lars Hierta Memorial Foundation, FO2012-1003
Available from: 2015-02-04 Created: 2015-02-04 Last updated: 2015-07-13Bibliographically approved

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Cohen, David
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