A numerical investigation of nonlinear Schrödinger equation using barycentric interpolation collocation method

In this paper, we will present a collocation approach based on barycentric interpolation functions and finite difference formulation to study the approximate solution of nonlinear Schrödinger equation. We discretize the time derivative by Crank-Nicolson scheme and bring barycentric interpolation functions into action for spatial discretization. Furthermore, consistency analysis of semi discrete collocation scheme is given. For the nonlinear term, we use Newton iterative method to derive the corresponding linear algebraic equations. Finally, numerical examples show that the numerical scheme has high precision and satisfies the mass and energy conservation.