Comparison of time splitting and backsubstitution methods for   integrating Vlasov's equation with magnetic fields
  The standard approach for integrating the multidimensional Vlasov equation using grid based, conservative schemes is based on a time splitting approach. Here, we show that although the truncation error is of second order, time splitting can introduce systematic heating of the plasma. We introduce a backsubstitution method, which not only avoids this deficiency but also is computationally less expensive. The general approach is demonstrated in conjunction with Boris' scheme for evaluating the characteristics. 
H. Schmitz and R. Grauer