Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
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 …