In the interest of time, I won't go through how one can numerically solve the telegraph model for velocity jump processes. A nice discussion of this is in Bill Young's lecture notes from the 1999 Summer Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution. To find this, go to GFD Proceedings Volumes choose your preference of postscript or pdf versions, then download Lecture 4 on Anomalous Diffusion. You'll find a discussion of the telegraph model and its numerical solution in Section 2 of this Lecture.