Convergence of the EBT method for a non-local model of cell proliferation with discontinuous interaction kernel

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dc.contributor.authorGwiazda, Piotr
dc.contributor.authorMiasojedow, Błażej
dc.contributor.authorSkrzeczkowski, Jakub
dc.contributor.authorSzymańska, Zuzanna
dc.contributor.organizationInstitute of Mathematics, Polish Academy of Sciences, Warsaw, Polanden
dc.contributor.organizationFaculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Polanden
dc.contributor.organizationInterdisciplinary Centre for Mathematical and Computational Modelling, University of Warsawen
dc.contributor.organizationInstitute of Mathematics, Polish Academy of Sciences, Warsaw, Polanden
dc.date.accessioned2023-07-10T15:31:34Z
dc.date.available2023-07-10T15:31:34Z
dc.date.issued2022-02-02
dc.description.abstractWe consider the EBT algorithm (a particle method) for the nonlocal equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel, which is not Lipschitz continuous, thus preventing the application of standard arguments. Therefore, we use the radial symmetry of the problem instead and transform it using spherical coordinates. The resulting equation has a Lipschitz kernel with only one singularity at zero. We introduce a new weighted flat norm and prove that the particle method converges in this norm. We also comment on the two-dimensional case that requires the application of the theory of measure spaces on general metric spaces and present numerical simulations confirming the theoretical results. In a companion paper we apply the Bayesian method to fit parameters to this model and study its theoretical properties.en
dc.description.sponsorshipB. Miasojedow, J. Skrzeczkowski, and Z. Szymańska acknowledge the support from the National Science Centre, Poland – grant No. 2017/26/M/ST1/00783. P. Gwiazda was supported by the National Science Centre, Poland – grant No. 2018/30/M/ST1/00423. The calculations were made with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling of the University of Warsaw under the computational grant no. G79-28.
dc.identifier.citationGwiazda, P., Miasojedow, B., Skrzeczkowski, J., Szymańska, Z. (2023). Convergence of the EBT method for a non-local model of cell proliferation with discontinuous interaction kernel, IMA Journal of Numerical Analysis, 43(1), 590–626. https://doi.org/10.1093/imanum/drab102en
dc.identifier.doi10.1093/imanum/drab102
dc.identifier.issn0272-4979
dc.identifier.issn1464-3642
dc.identifier.urihttps://open.icm.edu.pl/handle/123456789/22689
dc.language.isoen
dc.publisherOxford University Pressen
dc.rightsUznanie autorstwa 4.0 Międzynarodowe*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectparticle methoden
dc.subjectEBT algorithmen
dc.subjectmeasure solutionsen
dc.subjectflat metricen
dc.subjectnonlocal equationen
dc.subjectconvergence analysisen
dc.subjectcancer modellingen
dc.titleConvergence of the EBT method for a non-local model of cell proliferation with discontinuous interaction kernelen
dc.typearticleen
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