title: A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map.
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.
authors.affiliation: Anthropological Institute and Museum, Univ. of Zürich, Zürich, Switzerland.|Seminar for Applied Mathematics, ETH, Zürich, Switzerland.
authors.forename: W P
authors.identifier: 0000-0003-0307-8009
authors.initials: WP
authors.lastname: Petersen
authors.affiliation: Anthropological Institute and Museum, Univ. of Zürich, Zürich, Switzerland.
authors.forename: S
authors.initials: S
authors.lastname: Callegari
authors.affiliation: Institute for Computational Science, Univ. of Zürich, Zürich, Switzerland.
authors.forename: G R
authors.initials: GR
authors.lastname: Lake
authors.affiliation: Anthropological Institute and Museum, Univ. of Zürich, Zürich, Switzerland.
authors.forename: N
authors.initials: N
authors.lastname: Tkachenko
authors.affiliation: Anthropological Institute and Museum, Univ. of Zürich, Zürich, Switzerland.
authors.forename: J D
authors.initials: JD
authors.lastname: Weissmann
authors.affiliation: Anthropological Institute and Museum, Univ. of Zürich, Zürich, Switzerland.
authors.forename: Ch P E
authors.initials: CP
authors.lastname: Zollikofer
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D004641:Emigration and Immigration; D020342:Finite Element Analysis; D006801:Humans; D016014:Linear Models; D009716:Numerical Analysis, Computer-Assisted; D011156:Population Density; D011158:Population Growth