Free access article

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 Faou

INRIA, 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

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