A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
W P Petersen1,2, S Callegari1, G R Lake3
1Anthropological Institute and Museum, Univ. of Zürich, Zürich, Switzerland.
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.
Related Concept Videos
Modeling with Differential Equations
Population Growth
Growth Models with Integration: Problem Solving
Exponential Equations for Modeling Growth
Exponential Growth
Diffusion


