摘要
We consider in this paper a high-order,semi-Lagrangian technique to treat possibly degenerate advection-diffusion equations,which has been proposed in similar forms by various authors.The scheme is based on a stochastic representation formula for the solution,which allows to avoid the splitting between advective and diffusive part of the evolution operator.A general theoretical analysis is carried out in the paper,with a special emphasis on the possibility of using large Courant numbers,and numerical tests in one and two space dimensions are presented.
