Asymptotic-Preserving Scheme for the Resolution of Evolution Equations with Stiff Transport Terms

We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based on 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, models occurring in plasma physics. The asymptotic-preserving properties of our procedure permit us to study the long-time behavior of these models. Indeed, classical numerical approaches have to cope with large numerical errors in such time asymptotics, whereas our AP-procedure permits us to limit this drawback.