| Issue |
ESAIM: M2AN
Volume 51, Number 5, September-October 2017
|
|
|---|---|---|
| Page(s) | 1859 - 1882 | |
| DOI | https://doi.org/10.1051/m2an/2017010 | |
| Published online | 24 October 2017 | |
Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type
1 INRIA-Rennes, IRMAR, ENS Rennes, Campus de Beaulieu, 35042 Rennes cedex, France.
Philippe.Chartier@inria.fr
2 Université de Rennes 1, INRIA-Rennes, IRMAR, Campus de Beaulieu, 35042 Rennes cedex, France.
Florian.Mehats@univ-rennes1.fr
3 Leopold–Franzens Universität Innsbruck, Institut für Mathematik, Technikerstraße 13/VII, 6020 Innsbruck, Austria.
Mechthild.Thalhammer@uibk.ac.at
4 Wolfgang Pauli Institut c/o Universität Wien, Fakultät für Mathematik, Oskar–Morgenstern–Platz 1, 1090 Wien, Austria.
Yong.Zhang@univie.ac.at
Received: 11 April 2016
Revised: 11 February 2017
Accepted: 7 March 2017
The convergence behaviour of multi-revolution composition methods combined with time-splitting methods is analysed for highly oscillatory linear differential equations of Schrödinger type. Numerical experiments illustrate and complement the theoretical investigations.
Mathematics Subject Classification: 34K33 / 34G10 / 35Q41 / 65M12 / 65N15
Key words: Highly oscillatory differential equations / time-dependent Schrödinger equations / multi-revolution composition methods / operator splitting methods / local error / convergence
© EDP Sciences, SMAI 2017
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