On the convergence of a high-accuracy conservative scheme for the Zakharov equations

In this paper, a high-accuracy conservative difference scheme is presented to solve the initial-boundary value problem of the Zakharov equations, which preserves the original conservative properties. The proposed scheme is based on finite difference method. The scheme is second-order accuracy in time and fourth-order accuracy in space. A detailed numerical analysis of the scheme is presented including a convergence analysis result. Numerical examples are given to confirm the proposed scheme is efficient, reliable and of high accuracy.