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Free accessOther version: http://link.springer.com/10.1007/s00211-013-0602-0
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Scientific Article
unige:41957 
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Multi-revolution composition methods for highly oscillatory differential equations |
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| Authors | ||
| 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 map — Highly-oscillatory — Averaging — Differential equation — Composition method — Geometric integration — Asymptotic preserving | |
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Article (Author postprint) (681 Kb) - Free access Other version: http://link.springer.com/10.1007/s00211-013-0602-0 |
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| Structures | ||
| Research group | Analyse numérique | |
| Project | FNS: 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. https://archive-ouverte.unige.ch/unige:41957 |
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