Maximum norm error bound of a linearized difference scheme for a coupled nonlinear Schrِdinger equations

In this article, a linearized conservative difference scheme for a coupled nonlinear Schrِdinger equations is studied. The discrete energy method and an useful technique are used to analyze the difference scheme. It is shown that the difference solution unconditionally converges to the exact solution with second order in the maximum norm. Numerical experiments are presented to support the theoretical results.