Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776192 | Journal of Computational and Applied Mathematics | 2017 | 18 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Matthew A. Beauregard, Joshua Padgett, Rana Parshad,