The Numerical Analysis of the Long Time Asymptotic Behavior for Lotka-Volterra Competition Model with Diffusion. (26th April 2019)

• Record Type: Journal Article
• Authors: Wang, Jue; Liu, QinPan; Luo, YueSheng
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 6(2019)
• Page Start: 685
• Page End: 705
• Publication Date: 2019-04-26
• Subjects: Finite difference method -- long time behavior -- Lotka-Volterra competition -- reaction diffusion equation; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1566245
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we consider the long time asymptotic behavior of the Lotka-Volterra model with diffusion for two competing species by the finite difference method. The unique solvability and priori estimates of numerical solution for discrete systems are proved. On the basis of the priori estimates, the long time convergence and stability of the difference schemes are obtained, and the numerical convergence order isO ( τ 2 + h 2 ) in theL ∞ -norm. Furthermore, numerical results are also given in order to check the dynamic properties for the long-term development of populations.