Geometric integrators for piecewise smooth Hamiltonian systems
IPSO, INRIA-Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France. firstname.lastname@example.org
Revised: 5 September 2007
In this paper, we consider C1,1 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.
Mathematics Subject Classification: 65L05 / 65L06 / 65L20
Key words: Hamiltonian systems / symplecticity / volume-preservation / energy-preservation / B-splines / weak order.
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