The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equation (II)

Abstract

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors $\mathcal{A}_N$, $\mathcal{A}_N^k$ respectively and $d (\mathcal{A}_N, \mathcal{A})\to 0$, $d (\mathcal{A}_N^k, \mathcal{A}) \to 0$.