This talk is based on recent joint work with D. Iglesias and J.C. Marrero. Following O. Cosserat, we first review a general approach to approximate hamiltonian flows in a Poisson manifold. Only the "strict bi-realization" data is used in these approaches, but not the underlying groupoid multiplication. We then explain how multiplication "m" can be incorporated into this construction as well as how generating functions for m yield recurrence "multiplicative" approximation formulas. We describe the resulting practical numerical algorithms and some illustrative examples.