We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. I...We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d（Ah,τ, .A） → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.展开更多
基金The NSF (10871055) of Chinathe Fundamental Research Funds (HEUCFL20111102)for the Central Universities
文摘We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d（Ah,τ, .A） → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.
