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Geometric integrators for piecewise smooth Hamiltonian systems

Published online by Cambridge University Press:  27 March 2008

Philippe Chartier  and
Erwan Faou
Philippe Chartier
Affiliation:
IPSO, INRIA-Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France. chartier@irisa.fr
Erwan Faou
Affiliation:
IPSO, INRIA-Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France. chartier@irisa.fr
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Abstract

In this paper, we consider C 1,1 Hamiltonian systems. We prove the existence of a first derivative of the flow with respect to initial values and show that it satisfies the symplecticity condition almost everywhere in the phase-space. In a second step, we present a geometric integrator for such systems (called the SDH method) based on B-splines interpolation and a splitting method introduced by McLachlan and Quispel [Appl. Numer. Math. 45 (2003) 411–418], and we prove it is convergent, and that it preserves the energy and the volume.

Keywords

Hamiltonian systemssymplecticityvolume-preservationenergy-preservationB-splinesweak order.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 2 , March 2008 , pp. 223 - 241
Copyright
© EDP Sciences, SMAI, 2008

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