On the approximation of the Lotka–McKendrick equation with finite life-span

摘要

We consider the linear Lotka–McKendrick equation and discuss in detail how to solve the problem of the breakdown of the usual finite-difference methods when the mortality is unbounded. Usual error bounds require some derivative of the mortality rate to be bounded across all ages. Our approach works for a model class of mortality rates, and we show that not all methods are compatible with any mortality function.