Voir la notice de l'article provenant de la source Numdam
In this paper, we consider 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.
@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 },
pages = {223--241},
publisher = {EDP-Sciences},
volume = {42},
number = {2},
year = {2008},
doi = {10.1051/m2an:2008006},
mrnumber = {2405146},
zbl = {1145.65110},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008006/}
}
TY - JOUR AU - Chartier, Philippe AU - Faou, Erwan TI - Geometric integrators for piecewise smooth hamiltonian systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2008 SP - 223 EP - 241 VL - 42 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008006/ DO - 10.1051/m2an:2008006 LA - en ID - M2AN_2008__42_2_223_0 ER -
%0 Journal Article %A Chartier, Philippe %A Faou, Erwan %T Geometric integrators for piecewise smooth hamiltonian systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2008 %P 223-241 %V 42 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008006/ %R 10.1051/m2an:2008006 %G en %F M2AN_2008__42_2_223_0
Chartier, Philippe; Faou, Erwan. Geometric integrators for piecewise smooth hamiltonian systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 2, pp. 223-241. doi: 10.1051/m2an:2008006
Cité par Sources :