Volume 42, Number 2, March-April 2008
|Page(s)||223 - 241|
|Published online||27 March 2008|
Geometric integrators for piecewise smooth Hamiltonian systems
IPSO, INRIA-Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France. email@example.com
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.
© EDP Sciences, SMAI, 2008
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.