The Escalator Boxcar Train Method for a System of Aged-structured Equations in the Space of Measures

TL;DR

This paper extends the Escalator Boxcar Train (EBT) numerical method to a complex two-sex population model, proving its convergence in the space of measures and demonstrating its effectiveness through simulations.

Contribution

The paper derives a simplified EBT method for a coupled hyperbolic PDE system and proves its convergence in the measure space, expanding its applicability to more complex population models.

Findings

Convergence of the simplified EBT method is proven in the space of measures.

Numerical simulations confirm the theoretical convergence and effectiveness.

The method is applicable to coupled hyperbolic PDEs with nonlocal boundary conditions.

Abstract

The Escalator Boxcar Train (EBT) method is a well known and widely used numerical method for one-dimensional structured population models of McKendrick-von Foerster type. Recently the method, in its full generality, has been applied to aged-structured two-sex population model (Fredrickson-Hoppensteadt model), which consists of three coupled hyperbolic partial differential equations with nonlocal boundary conditions. We derive the simplified EBT method and prove its convergence to the solution of Fredrickson-Hoppensteadt model. The convergence can be proven, however only if we analyse the whole problem in the space of nonnegative Radon measures equipped with bounded Lipschitz distance (flat metric). Numerical simulations are presented to illustrate the results.