Numerical Solutions of Coupled Nonlinear Schrödinger Equations by Orthogonal Spline Collocation Method (Communications in Computational Physics, 2012)
In this paper, we present the use of the orthogonal spline collocationmethod for the semi-discretization scheme of the one-dimensional coupled nonlinear Schrödinger equations. This method uses the Hermite basis functions, by whichphysical quantities are approximated with their values and derivatives associated withGaussian points. The convergence rate with order O(h4+τ2) and the stability of thescheme are proved. Conservation properties are shown in both theory and practice.Extensive numerical experiments are presented to validate the numerical study underconsideration.