An Unconditionally Stable Numerical Scheme for a Competition System Involving Diffusion Terms

An Unconditionally Stable Numerical Scheme for a Competition System Involving Diffusion Terms

Year:    2020

Author:    Seth Armstrong, Jianlong Han

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 212–235

Abstract

A system of difference equations is proposed to approximate the solution of a system of partial differential equations that is used to model competing species with diffusion. The approximation method is a new semi-implicit finite difference scheme that is shown to mimic the dynamical properties of the true solution. In addition, it is proven that the scheme is uniquely solvable and unconditionally stable. The asymptotic behavior of the difference scheme is studied by constructing upper and lower solutions for the difference scheme. The convergence rate of the numerical solution to the true solution of the system is also given.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2020-IJNAM-13648

International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 212–235

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Competing species convergence asymptotic behavior implicit finite difference scheme.

Author Details

Seth Armstrong

Jianlong Han