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

W P Petersen, S Callegari, G R Lake, N Tkachenko, J D Weissmann and Ch P E Zollikofer

PLOS ONE, 2017, vol. 12, issue 1, 1-19

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0167514

DOI: 10.1371/journal.pone.0167514

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