Volume 29, Issue 1
Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization

Commun. Math. Res., 29 (2013), pp. 51-60.

Published online: 2021-05

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• 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.

• Keywords

Extended Fisher–Kolmogorov equation, finite difference method, global attractor, long time stability and convergence.

65M06, 37L99, 35B40, 35Q55, 65M20

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@Article{CMR-29-51, author = {Wang , Jue}, title = {Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19028.html} }
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 -

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.

Jue Wang. (2021). Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization. Communications in Mathematical Research . 29 (1). 51-60. doi:
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