Finite difference method for generalized Zakharov equations

A conservative difference scheme is presented for the initial-boundary value problem for generalized Zakharov equations. The scheme can be implicit or semiexplicit depending on the choice of a parameter. On the basis of a priori estimates and an inequality about norms, convergence of the difference solution is proved in order <IMG WIDTH="102" HEIGHT="43" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$ O({h^2} + {\tau ^2})$">, which is better than previous results.