On the convergence of the Escalator Boxcar Train

Åke Brännström, Linus Carlsson, Daniel Simpson

Research output: Contribution to journalArticlepeer-review

19 Citations (SciVal)


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 pages17
JournalSIAM Journal on Numerical Analysis
Issue number6
Publication statusPublished - 2013


  • math.NA
  • q-bio.PE


Dive into the research topics of 'On the convergence of the Escalator Boxcar Train'. Together they form a unique fingerprint.

Cite this