  Recently developed theoretical framework for analysis of structured
population dynamics in the spaces of nonnegative Radon measures with a suitable
metric provides a rigorous tool to study numerical schemes based on particle
methods. The approach is based on the idea of tracing growth and transport of
measures which approximate the solution of original partial differential
equation. In this paper we present analytical and numerical study of two
versions of Escalator Boxcar Train (EBT) algorithm which has been widely
applied in theoretical biology, and compare it to the recently developed
split-up algorithm. The novelty of this paper is in showing well-posedness and
convergence rates of the schemes using the concept of semiflows on metric
spaces. Theoretical results are validated by numerical simulations of test
cases, in which distances between simulated and exact solutions are computed
using flat metric.

Analysis of PDEs