Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations (Advances in Applied Mathematics and Mechanics, 2018)
In this paper we show a fourth-order compact split-step finite differencemethod to solve the two- and three-dimensional nonlinear Schrödinger equations. Theconservation properties and stability are analyzed for the proposed scheme. Numericalresults show that the method can provide accurate and stable solutions for thenonlinear Schrödinger equation.