Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations

Rena Eskar; Xinlong Feng; Pengzhan Huang

doi:10.4208/aamm.OA-2017-0162

Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations

Authors

Rena Eskar
Xinlong Feng
Pengzhan Huang

DOI:

https://doi.org/10.4208/aamm.OA-2017-0162

Keywords:

Nonlinear Schrödinger equation, operator splitting method, compact split-step finite difference method, conservation law, stability.

Abstract

In this paper we show a fourth-order compact split-step finite difference method to solve the two- and three-dimensional nonlinear Schrödinger equations. The conservation properties and stability are analyzed for the proposed scheme. Numerical results show that the method can provide accurate and stable solutions for the nonlinear Schrödinger equation.