  We are concerned with the convergence of a numerical scheme for the
initial-boundary value problem associated to the Korteweg-de Vries- Kawahara
equation (in short Kawahara equation), which is a transport equation perturbed
by dispersive terms of 3rd and 5th order. This equation appears in several uid
dynamics problems. It describes the evolution of small but finite amplitude
long waves in various problems in uid dynamics. We prove here the convergence
of both semi-discrete as well as fully-discrete finite difference schemes for
the Kawahara equation. Finally, the convergence is illustratred by several
examples.
