Numerical analysis for a conservative difference scheme to solve the Schrödinger-Boussinesq equation (Q633944)

A finite difference scheme for the solution of an initial-boundary value problem of the Schrödinger-Boussinesq equation is presented. The scheme is fully implicit and conserves two invariable quantities of the system. The existence of the solution for the scheme is investigated, the process for the numerical solution is described and convergence of an iteration method is proven. The uniqueness, convergence and stability for the difference solution are discussed. Numerical experiments verify the accuracy of the method.