A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
Petersen WPPapers in this archive, Callegari SPapers in this archive, Lake GRPapers in this archive, Tkachenko NPapers in this archive, Weissmann JDPapers in this archive, Zollikofer CPPapers in this archive
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.
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