Geometric integrators for piecewise smooth hamiltonian systems
Chartier, Philippe ; Faou, Erwan
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008), p. 223-241 / Harvested from Numdam
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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.

Publié le : 2008-01-01
DOI : https://doi.org/10.1051/m2an:2008006
Classification:  65L05,  65L06,  65L20 
@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},
     volume = {42},
     year = {2008},
     pages = {223-241},
     doi = {10.1051/m2an:2008006},
     mrnumber = {2405146},
     zbl = {1145.65110},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 42 (2008) pp. 223-241. doi : 10.1051/m2an:2008006. http://gdmltest.u-ga.fr/item/M2AN_2008__42_2_223_0/

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