On the convergence of the Escalator Boxcar Train

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/13730 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/13730 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/13730 archive 351 disk0/00/01/07/37 2016-01-15 08:49:58 2021-08-27 17:23:51 2016-01-15 08:49:58 monograph show 3 Brännström Å. 8085 Carlsson L. Simpson D. On the convergence of the Escalator Boxcar Train pub iis_ecl iis_met prog_eep 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. 2013 published IR-13-023 IR-13-023 39 public interim_report IIASA, Laxenburg, Austria 18 FALSE info:eu-repo/semantics/book