THERMAL SCIENCE

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Timothy G. Myers

,

Sarah L. Mitchell

APPLICATION OF THE HEAT-BALANCE AND REFINED INTEGRAL METHODS TO THE KORTEWEG-DE VRIES EQUATION

ABSTRACT
In this paper we consider approximate travelling wave solutions to the Korteweg-de Vries equation. The heat-balance integral method is first applied to the problem, using two different quartic approximating functions, and then the refined integral method is investigated. We examine two types of solution, chosen by matching the wave speed to that of the exact solution and by imposing the same area. The first set of solutions is generally better with an error that is fixed in time. The second set of solutions has an error that grows with time. This is shown to be due to slight discrepancies in the wave speed.
KEYWORDS
Korteweg-de Vries, heat-balance integral method, refined integral method, travelling wave
PAPER SUBMITTED: 2008-05-28
PAPER REVISED: 2008-06-20
PAPER ACCEPTED: 2008-09-25
DOI REFERENCE: https://doi.org/10.2298/TSCI0902113M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2009, VOLUME 13, ISSUE Issue 2, PAGES [113 - 119]
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Application of the heat-balance and refined integral methods to the Korteweg-de Vries equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence