High Order Maximum Principle Preserving Semi-Lagrangian Finite   Difference WENO schemes for the Vlasov Equation
  In this paper, we propose the parametrized maximum principle preserving (MPP) flux limiter, originally developed in [Z. Xu, Math. Comp., (2013), in press], to the semi- Lagrangian finite difference weighted essentially non-oscillatory scheme for solving the Vlasov equation. The MPP flux limiter is proved to maintain up to fourth order accuracy for the semi-Lagrangian finite difference scheme without any time step restriction. Numerical studies on the Vlasov-Poisson system demonstrate the performance of the proposed method and its ability in preserving the positivity of the probability distribution function while maintaining the high order accuracy. 
Tao Xiong and Jing-Mei Qiu and Zhengfu Xu and Andrew Christlieb
math.NA