| Abstract: | We present a numerical study of the long time behavior of approximation solution to the Extended Fisher–Kolmogorov equation with periodic boundaryconditions. The unique solvability of numerical solution is shown. It is proved thatthere exists a global attractor of the discrete dynamical system. Furthermore, weobtain the long-time stability and convergence of the difference scheme and the upper semicontinuity $d(mathcal{A}_{h,τ} ,mathcal{A}) → 0$. Our results show that the difference scheme caneffectively simulate the infinite dimensional dynamical systems. |
