# Geometric integrators for piecewise smooth Hamiltonian systems

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 2, page 223-241
- ISSN: 0764-583X

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topChartier, Philippe, and Faou, Erwan. "Geometric integrators for piecewise smooth Hamiltonian systems." ESAIM: Mathematical Modelling and Numerical Analysis 42.2 (2008): 223-241. <http://eudml.org/doc/250360>.

@article{Chartier2008,

abstract = {
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.
},

author = {Chartier, Philippe, Faou, Erwan},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Hamiltonian systems; symplecticity; volume-preservation; energy-preservation; B-splines; weak order.; weak order; convergence; splitting method; geometric integrator},

language = {eng},

month = {3},

number = {2},

pages = {223-241},

publisher = {EDP Sciences},

title = {Geometric integrators for piecewise smooth Hamiltonian systems},

url = {http://eudml.org/doc/250360},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Chartier, Philippe

AU - Faou, Erwan

TI - Geometric integrators for piecewise smooth Hamiltonian systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/3//

PB - EDP Sciences

VL - 42

IS - 2

SP - 223

EP - 241

AB -
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.

LA - eng

KW - Hamiltonian systems; symplecticity; volume-preservation; energy-preservation; B-splines; weak order.; weak order; convergence; splitting method; geometric integrator

UR - http://eudml.org/doc/250360

ER -

## References

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- R.I. McLachlan and G.R.W. Quispel, Geometric integration of conservative polynomial ODEs. Appl. Numer. Math.45 (2003) 411–418. Zbl1021.65064

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