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math.NA2019★ 4 cited
A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion
Matthew A. Beauregard, Joshua L. Padgett
Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowdin…
math.NA2015
A Nonlinear Splitting Algorithm for Systems of Partial Differential Equations with self-Diffusion
Matthew Beauregard, Joshua Padgett, Rana Parshad
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in the…
math.NA2014
Numerical Solutions to Singular Reaction-Diffusion Equation over Elliptical Domains
Matthew Alan Beauregard
Solid fuel ignition models, for which the dynamics of the temperature is independent of the single-species mass fraction, attempt to follow the dynamics of an explosive event. Such…