Abstract
In this paper, a numerical scheme for a nonlinear McKendrick–von Foerster equation with diffusion in age with the Dirichlet boundary condition, and the Robin boundary condition are proposed. The main idea to derive the scheme is to use the discretization based on the method of characteristics to the convection part, and the finite difference method to the rest of the terms. The nonlocal terms are dealt with the quadrature methods. As a result, an implicit scheme is obtained for the boundary value problem under consideration. The consistency, and the convergence of the proposed numerical scheme is established.
Acknowledgements
The authors would like to thank Prof. Jordi Ripoll for fruitful discussions. The authors are very grateful to the anonymous reviewers for their comments and suggestions that greatly helped to improve this manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).