A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map

We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling...

Descripción completa

Detalles Bibliográficos
Autores principales: Petersen, W. P., Callegari, S., Lake, G. R., Tkachenko, N., Weissmann, J. D., Zollikofer, Ch. P. E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2017
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5235379/
https://www.ncbi.nlm.nih.gov/pubmed/28085882
http://dx.doi.org/10.1371/journal.pone.0167514
_version_ 1782495145760915456
author Petersen, W. P.
Callegari, S.
Lake, G. R.
Tkachenko, N.
Weissmann, J. D.
Zollikofer, Ch. P. E.
author_facet Petersen, W. P.
Callegari, S.
Lake, G. R.
Tkachenko, N.
Weissmann, J. D.
Zollikofer, Ch. P. E.
author_sort Petersen, W. P.
collection PubMed
description We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas.
format Online
Article
Text
id pubmed-5235379
institution National Center for Biotechnology Information
language English
publishDate 2017
publisher Public Library of Science
record_format MEDLINE/PubMed
spelling pubmed-52353792017-02-06 A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map Petersen, W. P. Callegari, S. Lake, G. R. Tkachenko, N. Weissmann, J. D. Zollikofer, Ch. P. E. PLoS One Research Article We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas. Public Library of Science 2017-01-13 /pmc/articles/PMC5235379/ /pubmed/28085882 http://dx.doi.org/10.1371/journal.pone.0167514 Text en © 2017 Petersen et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Petersen, W. P.
Callegari, S.
Lake, G. R.
Tkachenko, N.
Weissmann, J. D.
Zollikofer, Ch. P. E.
A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
title A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
title_full A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
title_fullStr A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
title_full_unstemmed A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
title_short A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
title_sort stable finite-difference scheme for population growth and diffusion on a map
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5235379/
https://www.ncbi.nlm.nih.gov/pubmed/28085882
http://dx.doi.org/10.1371/journal.pone.0167514
work_keys_str_mv AT petersenwp astablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT callegaris astablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT lakegr astablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT tkachenkon astablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT weissmannjd astablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT zollikoferchpe astablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT petersenwp stablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT callegaris stablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT lakegr stablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT tkachenkon stablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT weissmannjd stablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap
AT zollikoferchpe stablefinitedifferenceschemeforpopulationgrowthanddiffusiononamap

Ejemplares similares