Year: 2018
Author: Abdelhamid Bezia, Ben Mabrouk Anouar
Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 3 : pp. 193–213
Abstract
This paper investigates a solution technique for solving a two-dimensional Kuramoto-Sivashinsky equation discretized using a finite difference method. It consists of an order reduction method into a coupled system of second-order equations, and to formulate the fully discretized, implicit time-marched system as a Lyapunov-Sylvester matrix equation. Convergence and stability is examined using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v31.n3.1
Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 3 : pp. 193–213
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Kuramoto-Sivashinsky equation