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arXiv · 1510.07694

A Nonlinear Splitting Algorithm for Systems of Partial Differential Equations with self-Diffusion

Matthew Beauregard·Joshua Padgett·Rana Parshad
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Abstract

Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular, self-diffusion is a nonlinear term that models overcrowding of a particular species. The nonlinearity complicates attempts to construct efficient and accurate numerical approximations of the underlying systems of equations. In this paper, a new nonlinear splitting algorithm is designed for a partial differential equation that incorporates self-diffusion. We present a general model that incorporates self-diffusion and develop a numerical approximation. The numerical analysis of the approximation provides criteria for stability and convergence. Numerical examples are used to illustrate the theoretical results.

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Matthew Beauregard, Joshua Padgett, Rana Parshad. 2015-10-26. A Nonlinear Splitting Algorithm for Systems of Partial Differential Equations with self-Diffusion. https://arxiv.org/abs/1510.07694

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