Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization
Year: 2013
Author: Jue Wang
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 51–60
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-CMR-19028
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 51–60
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Extended Fisher–Kolmogorov equation finite difference method global attractor long time stability and convergence.