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We consider a class of nonlinear partial-differential equations,
including the spatially homogeneous
Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules.
Continuing the work of [6, 7, 4],
we propose a probabilistic interpretation of such a
P.D.E. in terms of a
nonlinear stochastic differential equation driven by a standard
Brownian motion. We derive a numerical scheme, based on a system of
$n$ particles driven by $n$ Brownian motions,
and study its rate of convergence.
We finally deal with the possible extension of our numerical
scheme to the case of the Landau equation for soft potentials, and give
some numerical results.