Numerical Solutions of Coupled Nonlinear Schrödinger Equations by Orthogonal Spline Collocation Method

In this paper,we present the use of the orthogonal spline collocation method for the semi-discretization scheme of the one-dimensional coupled nonlinear Schrödinger equations.This method uses the Hermite basis functions,by which physical quantities are approximatedwith their values and derivatives associatedwith Gaussian points.The convergence rate with order O(h4+t2)and the stability of the scheme are proved.Conservation properties are shown in both theory and practice.Extensive numerical experiments are presented to validate the numerical study under consideration.