publication . Article . 2008

Geometric integrators for piecewise smooth Hamiltonian systems

Chartier, Philippe; Faou, Erwan;
Open Access English
  • Published: 01 Jan 2008
  • Publisher: HAL CCSD
Abstract
International audience; 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.
Subjects
free text keywords: weak order, B-splines, Hamiltonian systems, symplecticity, volume-preservation, energy-preservation, 65L05; 65L06; 65L20, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], Modelling and Simulation, Applied Mathematics, Analysis, Numerical Analysis, B-spline, Interpolation, Mathematics, Geometric integrator, Piecewise, Hamiltonian (quantum mechanics), symbols.namesake, symbols, Hamiltonian system, Mathematical analysis, Almost everywhere, Mathematical optimization
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publication . Article . 2008

Geometric integrators for piecewise smooth Hamiltonian systems

Chartier, Philippe; Faou, Erwan;