Abstract
The coupled nonlinear Schrödinger equation models several interesting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this article, we write a finite difference scheme to solve this equation. The method is fourth-order in space and second-order in time. It is unconditionally stable and extrapolation is used in the temporal direction and this makes the method fourth-order in the two directions, space and time. Many numerical tests have been conducted to display the robustness of the scheme.