A Conservative Difference Scheme for the Zakharov Equations

A new conservative difference scheme is presented for the periodic initial-value problem of Zakharov equations. The scheme can be implicit or semi-explicit, depending on the choice of a parameter. The discretization of the initial condition is of second-order accuracy, which is consistent with the accuracy of the scheme. On the basis of a priori estimates and an inequality about norms, convergence of the difference solutions is proved in the energy norm. Numerical experiments with the schemes are done for several test cases. Computational results demonstrate that the new semi-explicit scheme with a new initial approximation is more accurate and computationally efficient.