Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization

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.

Author Details

Jue Wang