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Scientific article
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English

Multi-revolution composition methods for highly oscillatory differential equations

Published inNumerische Mathematik, vol. 128, no. 1, p. 167-192
Publication date2014
Abstract

We introduce a new class of multi-revolution composition methods (MRCM) for the approximation of the Nth-iterate of a given near-identity map. When applied to the numerical integration of highly oscillatory systems of differential equations, the technique benefits from the properties of standard composition methods: it is intrinsically geometric and well-suited for Hamiltonian or divergence-free equations for instance. We prove error estimates with error constants that are independent of the oscillatory frequency. Numerical experiments, in particular for the nonlinear Schr¨odinger equation, illustrate the theoretical results, as well as the efficiency and versatility of the methods.

Keywords
  • Near-identity map
  • Highly-oscillatory
  • Averaging
  • Differential equation
  • Composition method
  • Geometric integration
  • Asymptotic preserving
Research group
Funding
  • Swiss National Science Foundation - 200020144313/1.
Citation (ISO format)
CHARTIER, Philippe et al. Multi-revolution composition methods for highly oscillatory differential equations. In: Numerische Mathematik, 2014, vol. 128, n° 1, p. 167–192. doi: 10.1007/s00211-013-0602-0
Main files (1)
Article (Accepted version)
accessLevelPublic
Identifiers
ISSN of the journal0029-599X
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Technical informations

Creation11/17/2014 3:30:00 PM
First validation11/17/2014 3:30:00 PM
Update time03/14/2023 10:16:09 PM
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