Convergence of a conservative difference scheme for a class of Klein-Gordon-Schrödinger equations in one space dimension

A conservative difference scheme is presented for the initial-boundary value problem of a class of Klein-Gordon-Schrödinger equations. The scheme can be implicit or implicit-explicit, depending on the choice of a parameter. On the basis of the priori estimates and an inequality about norms, convergence of the difference solution is proved with order O(h2+τ2) in the energy norm.