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

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...

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Bibliographic Details
Main Authors: W P Petersen, S Callegari, G R Lake, N Tkachenko, J D Weissmann, Ch P E Zollikofer
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2017-01-01
Series:PLoS ONE
Online Access:http://europepmc.org/articles/PMC5235379?pdf=render
Description
Summary: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.
ISSN:1932-6203

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