Uniformly accurate multiscale time integrators for second order oscillatory differential equations with large initial data

Xiaofei Zhao 1, 2, *
* Auteur correspondant
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We apply the modulated Fourier expansion to a class of second order differential equations which consists of an oscillatory linear part and a nonoscillatory nonlinear part, with the total energy of the system possibly unbounded when the oscillation frequency grows. We comment on the difference between this model problem and the classical energy bounded oscillatory equations. Based on the expansion, we propose the multiscale time integrators to solve the ODEs under two cases: the nonlinearity is a polynomial or the frequencies in the linear part are integer multiples of a single generic frequency. The proposed schemes are explicit and efficient. The schemes have been shown from both theoretical and numerical sides to converge with a uniform second order rate for all frequencies. Comparisons with popular exponential integrators in the literature are done.
Type de document :
Article dans une revue
BIT Numerical Mathematics, Springer Verlag, 2017, 57 (3), pp.649 - 683. 〈10.1007/s10543-017-0646-0〉
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https://hal.archives-ouvertes.fr/hal-01591333
Contributeur : Marie-Annick Guillemer <>
Soumis le : jeudi 21 septembre 2017 - 11:54:09
Dernière modification le : samedi 23 septembre 2017 - 01:06:01

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Xiaofei Zhao. Uniformly accurate multiscale time integrators for second order oscillatory differential equations with large initial data. BIT Numerical Mathematics, Springer Verlag, 2017, 57 (3), pp.649 - 683. 〈10.1007/s10543-017-0646-0〉. 〈hal-01591333〉

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