  In this article, a numerical scheme to find approximate solutions to the
McKendrick-Von Foerster equation with diffusion (M-V-D) is presented. The main
difficulty in employing the standard analysis to study the properties of this
scheme is due to presence of nonlinear and nonlocal term in the Robin boundary
condition in the M-V-D. To overcome this, we use the abstract theory of
discretizations based on the notion of stability threshold to analyze the
scheme. Stability, and convergence of the proposed numerical scheme are
established.
