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ESAIM: Proc., 2008, Vol. 22, pp. 234-239
DOI: 10.1051/proc:072227
Qualitative behavior of splitting methods for the linear Schrödinger equation in molecular dynamics
Guillaume Dujardin and Erwan FaouINRIA, Campus de Beaulieu, 35042 Rennes Cedex, France;
guillaume.dujardin@irisa.fr
erwan.faou@irisa.fr
(Published online: 1 February 2008)
Abstract
We present a normal form theorem for the propagator of a splitting method applied to a linear Schrödinger equation.
This result allows us to derive conservation properties for the numerical solutions provided by the method.
As a conclusion, we show numerical experiments illustrating our results.
Mathematics Subject Classification. 65P10, 37M15, 37K55
Key words: infinite-dimensional Hamiltonian systems, symplectic integrators, perturbation theory for infinite-dimensional systems
© EDP Sciences, ESAIM 2007