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Volume 13, Issue 3
Finite Difference Schemes for the Korteweg-de Vries-Kawahara Equation

U. Koley

Int. J. Numer. Anal. Mod., 13 (2016), pp. 344-367.

Published online: 2016-05

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  • 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.

  • Keywords

Kawahara Equation, finite difference scheme, implicit schemes, convergence, existence.

  • AMS Subject Headings

35Q53, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-344, author = {U. Koley}, title = {Finite Difference Schemes for the Korteweg-de Vries-Kawahara Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/443.html} }
TY - JOUR T1 - Finite Difference Schemes for the Korteweg-de Vries-Kawahara Equation AU - U. Koley JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 344 EP - 367 PY - 2016 DA - 2016/05 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/443.html KW - Kawahara Equation, finite difference scheme, implicit schemes, convergence, existence. AB -

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.

U. Koley. (2016). Finite Difference Schemes for the Korteweg-de Vries-Kawahara Equation. International Journal of Numerical Analysis and Modeling. 13 (3). 344-367. doi:
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