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Full-Text Articles in Physical Sciences and Mathematics
A Nonlinear Splitting Algorithm For Systems Of Partial Differential Equations With Self-Diffusion, Matthew Beauregard, Joshua L. Padgett, Rana D. Parshad
A Nonlinear Splitting Algorithm For Systems Of Partial Differential Equations With Self-Diffusion, Matthew Beauregard, Joshua L. Padgett, Rana D. Parshad
Faculty Publications
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 …
Biological Control Via "Ecological" Damping: An Approach That Attenuates Non-Target Effects, Rana D. Parshad, Kelly Black, Emmanuel Quansah, Matthew Beauregard
Biological Control Via "Ecological" Damping: An Approach That Attenuates Non-Target Effects, Rana D. Parshad, Kelly Black, Emmanuel Quansah, Matthew Beauregard
Faculty Publications
In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blowup in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach “disastrous” levels, in a finite time. We next propose various controls to drive down the invasive population growth and, in certain cases, eliminate blow-up. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer …