Using First order Backward Finite Difference technique, the trajectories of a projectile motion ( a bouncing ball) is solved for 2 cases: With and without the effect the air drag.
The air drag is assumed to be linear and uniform with a coefficient K. Also, the surface is assumed have a constant reflection coefficient of 0.5 (say).

For 1000 time steps ( iterations), the animation for the two cases is shown simultaneously .

The leftmost figure in the panel shows a screenshot of the animation.

The figure at the center shows the effect of bouncing for an ideal case ( no air drag, K=0) and for K=0,

The rightmost figure displays the projectile paths for different values of K, and without bouncing.

Animation : https://www.youtube.com/watch?v=KvdQtwMc34U