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Paper detail

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

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.

preprint2015arXivOpen access
W. P. PetersenS. CallegariN. TkachenkoJ. D. WeissmannCh. P. E. Zollikofer
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W. P. PetersenS. CallegariN. TkachenkoJ. D. WeissmannCh. P. E. Zollikofer

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