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arXiv · 1502.04483

A stable finite-difference scheme for growth and diffusion on a map

W. P. Petersen·S. Callegari·N. Tkachenko·J. D. Weissmann·Ch. P. E. Zollikofer
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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.

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W. P. Petersen, S. Callegari, N. Tkachenko, J. D. Weissmann, Ch. P. E. Zollikofer. 2015-02-16. A stable finite-difference scheme for growth and diffusion on a map. https://arxiv.org/abs/1502.04483

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