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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...
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.
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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