Solving coupled nonlinear Schrodinger equations using cubic B-spline interpolation and finite difference methods

The Coupled Nonlinear Schrodinger equations are solved numerically using the cubic B-spline (CuBS) interpolation method and finite difference method (FDM). The CuBS method is utilized as an interpolating function in the spatial dimension while the FDM is applied to discretize the temporal space. Applying the Von Neumann stability analysis, these schemes are tested to ensure their stabilities. A numerical example is discussed and compared with exact solutions and results from the FDM. It showed that CuBS interpolation method and FDM are very encouraging and can be conveniently used to solve problem.