  We are concerned with the convergence of spectral method for the numerical
solution of 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 fluid dynamics problems. It describes the evolution of small
but finite amplitude long waves in various problems in fluid dynamics. These
equations are discretized in space by the standard Fourier- Galerkin spectral
method and in time by the explicit leap-frog scheme. For the resulting fully
discrete, conditionally stable scheme we prove an L2-error bound of spectral
accuracy in space and of second-order accuracy in time.
