Geometric integrators for piecewise smooth hamiltonian systems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 2, p. 223-241

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.

DOI : https://doi.org/10.1051/m2an:2008006
Classification:  65L05,  65L06,  65L20
Keywords: hamiltonian systems, symplecticity, volume-preservation, energy-preservation, B-splines, weak order
@article{M2AN_2008__42_2_223_0,
author = {Chartier, Philippe and Faou, Erwan},
title = {Geometric integrators for piecewise smooth hamiltonian systems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {42},
number = {2},
year = {2008},
pages = {223-241},
doi = {10.1051/m2an:2008006},
zbl = {1145.65110},
mrnumber = {2405146},
language = {en},
url = {http://www.numdam.org/item/M2AN_2008__42_2_223_0}
}

Chartier, Philippe; Faou, Erwan. Geometric integrators for piecewise smooth hamiltonian systems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 2, pp. 223-241. doi : 10.1051/m2an:2008006. http://www.numdam.org/item/M2AN_2008__42_2_223_0/

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