Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation

Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation

Two numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference...

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Main Authors: Kanyuta Poochinapan, Ben Wongsaijai, Thongchai Disyadej
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2014/862403
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spelling doaj-00fc2cf0160647a988c392ea8e1c77b12020-11-24T23:47:11ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472014-01-01201410.1155/2014/862403862403Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries EquationKanyuta Poochinapan0Ben Wongsaijai1Thongchai Disyadej2Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandElectricity Generating Authority of Thailand, Phitsanulok 65000, ThailandTwo numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference methods. Linear stability analysis of two methods is presented by the Von Neumann analysis. The new methods give second- and fourth-order accuracy in time and space, respectively. The numerical experiments show that the proposed methods improve the accuracy of the solution significantly.http://dx.doi.org/10.1155/2014/862403
collection DOAJ
language English
format Article
sources DOAJ
author Kanyuta Poochinapan
Ben Wongsaijai
Thongchai Disyadej
spellingShingle Kanyuta Poochinapan
Ben Wongsaijai
Thongchai Disyadej
Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
Mathematical Problems in Engineering
author_facet Kanyuta Poochinapan
Ben Wongsaijai
Thongchai Disyadej
author_sort Kanyuta Poochinapan
title Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
title_short Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
title_full Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
title_fullStr Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
title_full_unstemmed Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
title_sort efficiency of high-order accurate difference schemes for the korteweg-de vries equation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2014-01-01
description Two numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference methods. Linear stability analysis of two methods is presented by the Von Neumann analysis. The new methods give second- and fourth-order accuracy in time and space, respectively. The numerical experiments show that the proposed methods improve the accuracy of the solution significantly.
url http://dx.doi.org/10.1155/2014/862403
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AT benwongsaijai efficiencyofhighorderaccuratedifferenceschemesforthekortewegdevriesequation
AT thongchaidisyadej efficiencyofhighorderaccuratedifferenceschemesforthekortewegdevriesequation
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