A higher order numerical scheme to a nonlinear McKendrick–Von Foerster equation with singular mortality

Abstract

In this paper, higher-order numerical schemes to the McKendrick–Von Foerster equation are presented when the death rate has singularity at the maximum age. The third, fourth-order schemes that are proposed here are based on the characteristics which are non-intersecting lines in this case, and are multi-step methods with appropriate corrections at each step. In fact, the convergence analysis of these schemes is discussed in detail. Moreover, numerical experiments are provided to validate the orders of convergence of the proposed third-order and fourth-order schemes.