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Multi-revolution composition methods for highly oscillatory differential equations

Chartier, Philippe
Makazaga, Joseba
Murua, Ander
Published in Numerische Mathematik. 2014, vol. 128, no. 1, p. 167-192
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 mapHighly-oscillatoryAveragingDifferential equationComposition methodGeometric integrationAsymptotic preserving
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Research group Analyse numérique
Project FNS: 200020144313/1.
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CHARTIER, Philippe et al. Multi-revolution composition methods for highly oscillatory differential equations. In: Numerische Mathematik, 2014, vol. 128, n° 1, p. 167-192. https://archive-ouverte.unige.ch/unige:41957

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Deposited on : 2014-11-18

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