Abstract
In this paper, we consider the two dimensional coupled nonlinear Schrodinger equation (CNLS). Anumerical scheme for solving the coupled system is derived, we present an Alternating Direction Implicit (ADI) (DouglasRachford) splitting method for solving the resulting scheme. An Iterative procedure is adopted for solving the nonlinear ADI method obtained. The scheme is of second order accuracy in space and first order in time. The Fourier stability analysis shows that the scheme is unconditional stable. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the scheme.