  An efficient numerical approach based on weighted average finite differences
is used to solve the Newtonian plane Couette flow with wall slip, obeying a
dynamic slip law that generalizes the Navier slip law with the inclusion of a
relaxation term. Slip is exhibited only along the fixed plate, and the motion
is triggered by the motion of the other plate. Three different cases are
considered for the motion of the moving plate, i.e., constant speed,
oscillating speed, and a single-period sinusoidal speed. The velocity and the
volumetric flow rate are calculated in all cases and comparisons are made with
the results of other methods and available results in the literature. The
numerical outcomes confirm the damping with time and the lagging effects
arising from the Navier and dynamic wall slip conditions and demonstrate the
hysteretic behavior of the slip velocity in following the harmonic boundary
motion.
