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Analysis of particle methods for structured population models with nonlocal boundary term in the framework of bounded Lipschitz distance
Author(s) -
Gwiazda Piotr,
Jabłoński Jędrzej,
MarciniakCzochra Anna,
Ulikowska Agnieszka
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21879
Subject(s) - mathematics , lipschitz continuity , bounded function , metric (unit) , partial differential equation , population , term (time) , convergence (economics) , metric space , boundary (topology) , numerical analysis , mathematical analysis , sociology , economics , economic growth , operations management , physics , demography , quantum mechanics
Recently developed theoretical framework for analysis of structured population dynamics in the spaces of nonnegative Radon measures with a suitable metric provides a rigorous tool to study numerical schemes based on particle methods. The approach is based on the idea of tracing growth and transport of measures which approximate the solution of original partial differential equation. In this article, we present analytical and numerical study of two versions of Escalator Boxcar Train algorithm which has been widely applied in theoretical biology, and compare it to the recently developed split‐up algorithm. The novelty of this article is in showing well‐posedness and convergence rates of the schemes using the concept of semiflows on metric spaces. Theoretical results are validated by numerical simulations of test cases, in which distances between simulated and exact solutions are computed using flat metric. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1797–1820, 2014