THERMAL SCIENCE

International Scientific Journal

COMPACT SCHEMES FOR KORTEWEG-DE VRIES EQUATION

ABSTRACT
This paper proposes one family of compact schemes for Korteweg-de Vries equation. In the deterministic case, the schemes are convergent with fourth-order accuracy both in space and in time. Moreover, the schemes are stable. The numerical dispersion relation is analyzed. We compare the schemes with one second-order scheme. The numerical examples test the effect of the schemes. In the stochastic case, we simulate the wave profile and three discrete dynamical quantities for Korteweg-de Vries equation with small noise. The white noise has stochastic influence on the profile and dynamical quantities of the solution. If the size of noise increases, the perturbation on the profile and dynamical quantities will increase accordingly.
KEYWORDS
PAPER SUBMITTED: 2016-06-13
PAPER REVISED: 2016-08-05
PAPER ACCEPTED: 2017-05-19
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI160612071Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE 4, PAGES [1797 - 1806]
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© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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