Convergence of Semi-discrete Stationary Wigner Equation with Inflow   Boundary Conditions
  Making use of the Whittaker-Shannon interpolation formula with shifted sampling points, we propose in this paper a well-posed semi-discretization of the stationary Wigner equation with inflow BCs. The convergence of the solutions of the discrete problem to the continuous problem is then analysed, providing certain regularity of the solution of the continuous problem. 
Ruo Li, Tiao Lu and Zhangpeng Sun
math.NA