Geodesic
Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type
Chartier, Philippe1  ; Méhats, Florian2  ; Thalhammer, Mechthild3 ; Zhang, Yong4
1 INRIA-Rennes, IRMAR, ENS Rennes, Campus de Beaulieu, 35042 Rennes cedex, France.
2 Université de Rennes 1, INRIA-Rennes, IRMAR, Campus de Beaulieu, 35042 Rennes cedex, France.
3 Leopold–Franzens Universität Innsbruck, Institut für Mathematik, Technikerstraße 13/VII, 6020 Innsbruck, Austria.
4 Wolfgang Pauli Institut c/o Universität Wien, Fakultät für Mathematik, Oskar–Morgenstern–Platz 1, 1090 Wien, Austria.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1859-1882

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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.

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Accepté le :
DOI : 10.1051/m2an/2017010
Classification : 34K33, 34G10, 35Q41, 65M12, 65N15
Keywords: Highly oscillatory differential equations, time-dependent Schrödinger equations, multi-revolution composition methods, operator splitting methods, local error, convergence

Chartier, Philippe 1 ; Méhats, Florian 2 ; Thalhammer, Mechthild 3 ; Zhang, Yong 4

1 INRIA-Rennes, IRMAR, ENS Rennes, Campus de Beaulieu, 35042 Rennes cedex, France.
2 Université de Rennes 1, INRIA-Rennes, IRMAR, Campus de Beaulieu, 35042 Rennes cedex, France.
3 Leopold–Franzens Universität Innsbruck, Institut für Mathematik, Technikerstraße 13/VII, 6020 Innsbruck, Austria.
4 Wolfgang Pauli Institut c/o Universität Wien, Fakultät für Mathematik, Oskar–Morgenstern–Platz 1, 1090 Wien, Austria. 
@article{M2AN_2017__51_5_1859_0,
     author = {Chartier, Philippe and M\'ehats, Florian and Thalhammer, Mechthild and Zhang, Yong},
     title = {Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of {Schr\"odinger} type},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1859--1882},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {5},
     year = {2017},
     doi = {10.1051/m2an/2017010},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017010/}
}
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Chartier, Philippe; Méhats, Florian; Thalhammer, Mechthild; Zhang, Yong. Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1859-1882. doi: 10.1051/m2an/2017010

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