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On the convergence of the Escalator Boxcar Train
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria.
2013 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, no 6, 3213-3231 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics , 2013. Vol. 51, no 6, 3213-3231 p.
Keyword [en]
escalator boxcar train, convergence, physiologically structured population models, measure-valued solutions, transport equation, particle methods
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-84438DOI: 10.1137/120893215OAI: oai:DiVA.org:umu-84438DiVA: diva2:684029
Available from: 2014-01-07 Created: 2014-01-07 Last updated: 2014-02-07Bibliographically approved

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Brännström, ÅkeCarlsson, LinusSimpson, Daniel
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