Travelling Wave Solution of the Kuramoto-Sivashinsky Equation: A Computational Study

被引：0

作者：

Aderogba, A. A. ^{[1
]}

Chapwanya, M. ^{[1
]}

Djoko, J. K. ^{[1
]}

机构：

[1] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B | 2012年 / 1479卷

关键词：

Kuramoto-Sivashinsky equation; travelling wave solution; time-step splitting;

D O I：

10.1063/1.4756252

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work considers the numerical solution of the Kuramoto-Sivashinsky equation using the fractional time splitting method. We will investigate the numerical behavior of two categories of the traveling wave solutions documented in the literature (Hooper & Grimshaw (1998)), namely: the regular shocks and the oscillatory shocks. We will also illustrate the ability of the scheme to produce convergent chaotic solutions.

引用

页码：777 / 780

页数：4

共 8 条

[1]

Adebayo A.A., 2012, J COMP PHYS UNPUB

[2] The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions [J].

Caglar, HN ;

Caglar, SH ;

Twizell, EH .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1999, 71 (03) :373-381

[3] TRAVELING WAVE SOLUTIONS OF THE KURAMOTO-SIVASHINSKY EQUATION [J].

HOOPER, AP ;

GRIMSHAW, R .

WAVE MOTION, 1988, 10 (05) :405-420

[4] Dynamical patterns in directional solidification [J].

Kassner, K ;

Hobbs, AK ;

Metzener, P .

PHYSICA D-NONLINEAR PHENOMENA, 1996, 93 (1-2) :23-51

[5]

KURAMOTO Y, 1978, SUP PROG THEOR PHYS, P346, DOI 10.1143/PTPS.64.346

[6] Optimal bounds on the Kuramoto-Sivashinsky equation [J].

Otto, Felix .

JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 257 (07) :2188-2245

[7] PREDICTING CHAOS FOR INFINITE DIMENSIONAL DYNAMIC-SYSTEMS - THE KURAMOTO-SIVASHINSKY EQUATION, A CASE-STUDY [J].

SMYRLIS, YS ;

PAPAGEORGIOU, DT .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1991, 88 (24) :11129-11132

[8] Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations [J].

Xu, Yan ;

Shu, Chi-Wang .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (25-28) :3430-3447

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