A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition

In this article, a numerical scheme to find approximate solutions to the McKendrick-Von Foerster equation with diffusion (M-V-D) is presented. This is a nonlinear equation for continuously structured population models. The main difficulty in employing the standard analysis to study the properties of this scheme is due to the 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. Finally, some numerical experiments are illustrated.