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Modulated Fourier expansions of highly oscillatory differential equations

Published inFoundations of computational mathematics, vol. 3, no. 4, p. 327-345
Publication date2003
Abstract

Modulated Fourier expansions are developed as a tool for gaining insight into the long-time behaviour 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 discretizations.

Keywords
  • Modulated Fourier expansion
  • Fermi-Past-Ulam problem
  • Conservation of energy
  • Highly oscillatory differential equations
Citation (ISO format)
COHEN, David, HAIRER, Ernst, LUBICH, Christian. Modulated Fourier expansions of highly oscillatory differential equations. In: Foundations of computational mathematics, 2003, vol. 3, n° 4, p. 327–345. doi: 10.1007/s10208-002-0062-x
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ISSN of the journal1615-3375
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