A stable finite-difference scheme for growth and diffusion on a map
Numerical Analysis
2015-02-17 v1
Abstract
We describe a general Godunov type splitting for numerical simulations of the Fisher/Kolmogorov-Petrovski-Piskunov growth and diffusion equation in two spatial dimensions. In particular, the method is appropriate for modeling population growth and dispersal on a terrestrial map. The procedure is semi-implicit, hence quite stable, and approximately second order accurate, excluding boundary condition complications. It also has low memory requirements and shows good performance. We illustrate an application of this solver: global human dispersal in the late Pleistocene, modeled via growth and diffusion over geographical maps of paleovegetation and paleoclimate.
Cite
@article{arxiv.1502.04483,
title = {A stable finite-difference scheme for growth and diffusion on a map},
author = {W. P. Petersen and S. Callegari and N. Tkachenko and J. D. Weissmann and Ch. P. E. Zollikofer},
journal= {arXiv preprint arXiv:1502.04483},
year = {2015}
}
Comments
27 pages, 12 figures