On the convergence of the Escalator Boxcar Train

Åke Brännström, Linus Carlsson, Daniel Simpson

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)

Abstract

The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical biology to investigate the dynamics of physiologically structured population models, i.e., models in which individuals differ by size or other physiological characteristics. The method was developed more than two decades ago, but has so far resisted attempts to give a formal proof of convergence. Using a modern framework of measure-valued solutions, we investigate the EBT method and show that the sequence of approximating solution measures generated by the EBT method converges weakly to the true solution measure under weak conditions on the growth rate, birth rate, and mortality rate. In rigorously establishing the convergence of the EBT method, our results pave the way for wider acceptance of the EBT method beyond theoretical biology and constitutes an important step towards integration with established numerical schemes.

Original languageEnglish
Pages (from-to)3213-3231
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number6
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Convergence
  • Escalator boxcar train
  • Measure-valued solutions
  • Particle methods
  • Physiologically structured population models
  • Transport equation

Cite this