11 citations · 54 across the 16 of their papers we have counts for
8 papers · 1 filter
Continuous versus discrete structures I -- Discrete embeddings and ordinary differential equations
Jacky Cresson, Frédéric Pierret
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of cat…
Coupling the non-gravitational forces and Modified Newton Dynamics for cometary orbits
Lucie Maquet, Frédéric Pierret
In recent work (Milgrom 2009, Blanchet & Novak 2011), the authors showed that MOdified Newton Dynamics (MOND) have a non-negligible secular perturbation effect on planets with larg…
A nonstandard Euler-Maruyama scheme
Frédéric Pierret
We construct a nonstandard finite difference numerical scheme to approximate stochastic differential equations (SDEs) using the idea of weighed step introduced by R.E. Mickens. We…
Non standard finite difference scheme preserving dynamical properties
Jacky Cresson, Frédéric Pierret
We study the construction of a non-standard finite differences numerical scheme for a general class of two dimensional differential equations including several models in population…
Helmholtz theorem for Hamiltonian systems on time scales
Frédéric Pierret
We derive the Helmholtz theorem for Hamiltonian systems defined on time scales in the context of nonshifted calculus of variations which encompass the discrete and continuous case.…
Dynamics of a rotating ellipsoid with a stochastic flattening
Etienne Behar, Jacky Cresson, Frédéric Pierret
Experimental data suggest that the Earth short time dynamics is related to stochastic fluctuation of its shape. As a first approach to this problem, we derive a toy-model for the m…
Stochastic Gauss Equations
Frédéric Pierret
We derive the equations of celestial mechanics governing the variations of the orbital elements under a stochastic perturbation generalizing the classical Gauss equations. Explicit…
The Sharma-Parthasarathy stochastic two-body problem
Jacky Cresson, Frédéric Pierret, Bénédicte Puig
We study the Sharma-Parthasarathy stochastic two-body problem introduced by N. Sharma and H. Parthasarathy in \cite{sharma}. In particular, we focus on the preservation of some fun…