Numerical analysis for a conservative difference scheme to solve the Schrödinger–Boussinesq equation

In this paper, we present a finite difference scheme for the solution of an initial-boundary value problem of the Schrödinger–Boussinesq equation. The scheme is fully implicit and conserves two invariable quantities of the system. We investigate the existence of the solution for the scheme, give computational process for the numerical solution and prove convergence of iteration method by which a nonlinear algebra system for unknown Vn+1 is solved. On the basis of a priori estimates for a numerical solution, the uniqueness, convergence and stability for the difference solution is discussed. Numerical experiments verify the accuracy of our method.