High order time discretization for backward semi-Lagrangian methods

We introduce different high order time discretization schemes for backward semi-Lagrangian methods. These schemes are based on multi-step schemes like Adams–Moulton and Adams–Bashforth schemes combined with backward finite difference schemes. We apply these methods to transport equations for plasma physics applications and for the numerical simulation of instabilities in fluid mechanics. In the context of backward semi-Lagrangian methods, this time discretization strategy is particularly efficient and accurate when the spatial error discretization becomes negligible and allows to use large time steps.