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Geometric integrators for piecewise smooth Hamiltonian systems

Philippe ChartierErwan Faou — 2008

ESAIM: Mathematical Modelling and Numerical Analysis

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 method) based on B-splines interpolation and a splitting method introduced by McLachlan and Quispel [.  (2003) 411–418], and we prove it is convergent, and that it preserves...

Raman laser : mathematical and numerical analysis of a model

François CastellaPhilippe ChartierErwan FaouDominique BayartFlorence LeplingardCatherine Martinelli — 2004

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.

Raman laser: mathematical and numerical analysis of a model

François CastellaPhilippe ChartierErwan FaouDominique BayartFlorence LeplingardCatherine Martinelli — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.

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