TY - JOUR
T1 - Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization
AU - Wang , Jue
JO - Communications in Mathematical Research 
VL - 1
SP - 51
EP - 60
PY - 2021
DA - 2021/05
SN - 29
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19028.html
KW - Extended Fisher–Kolmogorov equation, finite difference method, global
attractor, long time stability and convergence.
AB - <p style="text-align: justify;">We present a numerical study of the long time behavior of approximation 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 $d(\mathcal{A}_{h,τ} ,\mathcal{A}) → 0$. Our results show that the difference scheme can
effectively simulate the infinite dimensional dynamical systems.</p>