  Goal of this paper is to investigate several numerical schemes for the
resolution of two anisotropic Vlasov equations. These two toy-models arise from
a kinetic description of a tokamak plasma confined by strong magnetic fields.
The simplicity of our toy-models permits to better understand the features of
each scheme, in particular to investigate their asymptotic-preserving
properties, in the aim to choose then the most adequate numerical scheme for
upcoming, more realistic simulations.
