Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 344–367
Abstract
We are concerned with the convergence of fully discrete finite difference schemes for the Korteweg-de Vries-Kawahara equation, which is a transport equation perturbed by dispersive terms of third and fifth order. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0} = u_0$ are of high regularity, $u_0\in H^5(\mathbb{R})$, the schemes are shown to converge to a classical solution. Finally, the convergence is illustrated by an example.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-443
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 344–367
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Kawahara Equation finite difference scheme implicit schemes convergence existence.