A numerical scheme to the McKendrick–von Foerster equation with diffusion in age

Abstract

In this paper a numerical scheme for McKendrick–von Foerster equation with diffusion in age (MV-D) is proposed. First, we discretize the time variable to get a second-order ordinary differential equation (ODE). At each time level, well-posedness of this ODE is established using classical methods. Stability estimates for this semidiscrete scheme are derived. Later we construct piecewise linear (in time) functions using the solutions of the semidiscrete problems to approximate the solution to MV-D and establish the convergence result. Numerical results are presented in some cases and compared with the corresponding analytic solutions where the latter is known explicitly.