  We develop an asymptotic-preserving scheme to solve evolution problems
containing stiff transport terms. This scheme is based to a micro-macro
decomposition of the unknown, coupled with a stabilization procedure. The
numerical method is applied to the Vlasov equation in the gyrokinetic regime
and to the Vlasov-Poisson 1D1V equation, which occur in plasma physics. The
asymptotic-preserving properties of our procedure permit to study the long-time
behavior of these models. In particular, we limit drastically by this method
the numerical pollution, appearing in such time asymptotics when using
classical numerical schemes.
