The Numerical Analysis of the Long Time Asymptotic Behavior for Lotka-Volterra Competition Model with Diffusion

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 is in the -norm. Furthermore, numerical results are also given in order to check the dynamic properties for the long-term development of populations.