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

被引：6

作者：

Bezia, Abdelhamid ^{[1
]}

Mabrouk, Anouar Ben ^{[2
,3
,4
]}

机构：

[1] Univ Sci & Technol Houari Boumediene, Algebra & Number Theory Lab, Fac Math, BP 32, Algiers 16111, Algeria

[2] Inst Super Math Appl & Informat Kairouan, Dept Math, Ave Assad Ibn Al Fourat, Kairouan 3100, Tunisia

[3] Univ Monastir, Number Theory & Nonlinear Anal Dept Math, Lab Algebra, Fac Sci, Monastir 5000, Tunisia

[4] Tabuk Univ, Dept Math, Coll Sci, Tabuk, Saudi Arabia

来源：

JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 31卷 / 03期

关键词：

Kuramoto-Sivashinsky equation; Finite difference method; Lyapunov-Sylvester operators;

D O I：

10.4208/jpde.v31.n3.1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：193 / 213

页数：21

共 33 条

[11]

Il'yashenko Ju. S., 1992, Journal of Dynamics and Differential Equations, V4, P585, DOI 10.1007/BF01048261

[12] SOLUTION OF EQUATION AX + XB = C BY INVERSION OF AN M X M OR N X N MATRIX [J].