The Escalator Boxcar Train Method for a System of Aged-structured Equations in the Space of Measures
This work provides a rigorous convergence proof for a numerical method applied to a specific structured population model, which is an incremental theoretical contribution.
The authors derive a simplified Escalator Boxcar Train (EBT) method for the Fredrickson-Hoppensteadt two-sex population model and prove its convergence in the space of Radon measures with the bounded Lipschitz distance. Numerical simulations illustrate the results.
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.