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arXiv · 1901.06049

A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion

Matthew A. Beauregard·Joshua L. Padgett
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Abstract

Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self- and cross-diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy.

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Matthew A. Beauregard, Joshua L. Padgett. 2019-01-18. A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion. https://doi.org/10.1002/num.22315

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