A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
Petersen WP, Callegari S, Lake GR, Tkachenko N, Weissmann JD, Zollikofer CP.
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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