Geodesic
Geometric integrators for piecewise smooth hamiltonian systems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 2, pp. 223-241

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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.

DOI : 10.1051/m2an:2008006
Classification : 65L05, 65L06, 65L20
Keywords: hamiltonian systems, symplecticity, volume-preservation, energy-preservation, B-splines, weak order 
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     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/}
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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

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