Finite difference method for generalized Zakharov equations

Abstract

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 O ( h 2 + τ 2 ) O({h^2} + {\tau ^2}) , which is better than previous results.