The Korteweg-de Vries equation and the abcd-Boussinesq system are two hyperbolic-dispersive systems frequently used in hydrodynamics to describe the small amplitude, long wavelength shallow-water waves. We discretize these two models through a finite difference method and study the convergence. Particular attention will be paid to the L2-stability for which the nonlinear hyperbolic term and the dispersive one must be taken into account simultaneously. Moreover, the convergence order of the scheme will be quantified by the Sobolev regularity of the initial datum. It is a joint work with Cosmin Burtea, Frédéric Lagoutière and Frédéric Rousset.