11 citations · 54 across the 16 of their papers we have counts for
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Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
Jacky Cresson, Frédéric Pierret
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inver…
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…
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…