Volume 17, Issue 2
An Unconditionally Stable Numerical Scheme for a Competition System Involving Diffusion Terms

Seth Armstrong & Jianlong Han

Int. J. Numer. Anal. Mod., 17 (2020), pp. 212-235.

Published online: 2020-02

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  • 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.

  • Keywords

Competing species, convergence, asymptotic behavior, implicit finite difference scheme.

  • AMS Subject Headings

35B40, 35K60, 65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

armstrong@suu.edu (Seth Armstrong)

han@suu.edu (Jianlong Han)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-17-212, author = {Armstrong , Seth and Han , Jianlong}, title = {An Unconditionally Stable Numerical Scheme for a Competition System Involving Diffusion Terms}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13648.html} }
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 -

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.

Seth Armstrong & Jianlong Han. (2020). An Unconditionally Stable Numerical Scheme for a Competition System Involving Diffusion Terms. International Journal of Numerical Analysis and Modeling. 17 (2). 212-235. doi:
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