  A method of solution of the collisionless Vlasov equation, by following
collisionless phase point trajectories in phase space, is presented. It is
shown that by increasing the number of phase points, without enhancing the
resolution of phase space grid, the accuracy of simulation will be improved.
Besides, the phase points spacing introduces a smaller scale than grid spacing
on which fine structures might be more conveniently handled. In order to
perform simulation with a large population of phase points, an effective
interpolation scheme is introduced that reduces the number of operations. It is
shown that by randomizing initial position of the phase points along velocity
axis, the recurrence effect does not happen. Finally, the standard problem of
linear Landau damping will be examined.
