A compact split-step finite difference method for solving the nonlinear Schrodinger equations with constant and variable coefficients
A compact split-step finite difference method for solving the nonlinear Schrodinger equations with constant and variable coefficients
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DOI：
10.1016/j.cpc.2009.08.015
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发表时间：
2010-01-01
影响因子：
6.3
通讯作者：
Taleei, Ameneh
中科院分区：
文献类型：
--
作者：
Dehghan, Mehdi;Taleei, Ameneh
我们提出了一种紧凑的分步有限差分方法来求解具有常系数和变系数的非线性薛定谔方程。该方法通过引入空间变量离散化的紧凑方案，提高了分步有限差分法的精度，同时这种改进不会减小稳定范围，也不会增加计算成本。该方法还保留了一些守恒定律。利用常系数和变系数的三次非线性薛定谔方程和Gross-Pitaevskii方程进行了数值试验，以验证新数值方法的理论结果。 (C) 2009 Elsevier B.V. 保留所有权利。
We propose a compact split-step finite difference method to solve the nonlinear Schrodinger equations with constant and variable coefficients. This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical method by using the cubic nonlinear Schrodinger equation with constant and variable coefficients and Gross-Pitaevskii equation. (C) 2009 Elsevier B.V. All rights reserved.