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 - <p style="text-align: justify;">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.</p>