An efficient spline scheme of the coupled nonlinear Schrödinger equations

We construct an efficient numerical scheme for the coupled nonlinear Schrödinger equations by using adaptive spline function. We use the Crank–Nicolson scheme to discretize the time variables and the adaptive spline function to discretize spatial variables. The problem is reduced to a system of matrix equation iteration. We theoretically give stability analysis and numerically prove the law of conservation of energy. Numerical simulations are performed to demonstrate the effectiveness of the method.