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A stable finite-difference scheme for population growth and diffusion on a map


Petersen, Wesley P; Callegari, Simone; Tkachenko, Natalie; Weissmann, J D; Zollikofer, C P E (2017). A stable finite-difference scheme for population growth and diffusion on a map. PLoS ONE, 12(1):e0167514.

Abstract

We describe a general Godunov-type splitting for numerical simulations of the Fisher-Kolmogorov-Petrovski-Piskunov growth and diffusion equation in two spatial dimensions with Neumann boundary conditions. In particular, the method is appropriate for modeling population growth and dispersal on a terrestrial map. The procedure is semi-implicit, hence quite stable, and approximately O(x^2)+O(t^2) accurate, excluding boundary condition complications. It also has low memory requirements and shows good performance. Our principal application of this solver is global human dispersal in the late Pleistocene, modeled via growth and diffusion over geographical maps of changing paleovegetation and paleoclimate.

Abstract

We describe a general Godunov-type splitting for numerical simulations of the Fisher-Kolmogorov-Petrovski-Piskunov growth and diffusion equation in two spatial dimensions with Neumann boundary conditions. In particular, the method is appropriate for modeling population growth and dispersal on a terrestrial map. The procedure is semi-implicit, hence quite stable, and approximately O(x^2)+O(t^2) accurate, excluding boundary condition complications. It also has low memory requirements and shows good performance. Our principal application of this solver is global human dispersal in the late Pleistocene, modeled via growth and diffusion over geographical maps of changing paleovegetation and paleoclimate.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Department of Anthropology
Dewey Decimal Classification:300 Social sciences, sociology & anthropology
Language:English
Date:2017
Deposited On:06 Dec 2016 15:40
Last Modified:27 Apr 2017 06:50
Publisher:Public Library of Science (PLoS)
ISSN:1932-6203
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1371/journal.pone.0167514
Related URLs:http://www.aim.uzh.ch/de/research/cap/Publications/pub-zolli.html (Author)

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