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Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation

Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation
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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

Author Details

Abdelhamid Bezia

Ben Mabrouk Anouar

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