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

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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.

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

10.4208/aamm.OA-2017-0162

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[1]
2018. Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations. Advances in Applied Mathematics and Mechanics. 10, 4 (Sept. 2018), 879–895. DOI:https://doi.org/10.4208/aamm.OA-2017-0162.