TY - JOUR
T1 - An Unconditionally Stable Numerical Scheme for a Competition System Involving Diffusion Terms
AU - Armstrong , Seth
AU - Han , Jianlong
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 212
EP - 235
PY - 2020
DA - 2020/02
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13648.html
KW - Competing species, convergence, asymptotic behavior, implicit finite difference scheme.
AB - <p style="text-align: justify;">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.</p>