|本期目录/Table of Contents|

[1]靳珊,梁宗旗.分数阶非线性Schrodinger方程的时间分裂算法[J].集美大学学报(自然科学版),2018,23(1):63-69.
　JIN Shan,LIANG Zongqi.Timesplitting Method for the Fractional Nonlinear Schrodinger Equation[J].Journal of Jimei University,2018,23(1):63-69.
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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

卷:
第23卷
期数:
2018年第1期
页码:
63-69
栏目:
数理科学与信息工程
出版日期:
2018-01-28

文章信息/Info

Title:
Timesplitting Method for the Fractional Nonlinear Schrodinger Equation
作者:
靳珊; 梁宗旗
（集美大学理学院，福建 厦门 361021）
Author(s):
JIN Shan; LIANG Zongqi
(School of Science,Jimei University,Xiamen 361021,China)
关键词:
分数阶非线性Schrodinger方程; 分裂算法; 守恒律; 收敛性; 数值实验
Keywords:
fractional nonlinear Schrodinger equation; split method; conservation; convergence;  numerical experiment
分类号:
-
DOI:
-
文献标志码:
A
摘要:
主要研究分数阶非线性Schrodinger方程的时间分裂算法，将分数阶非线性Schrodinger方程分裂成一个线性方程和一个非线性方程分别求解。其中，非线性方程可精确求解，并满足“点点守恒”，而线性方程利用CrankNicolson差分格式离散求解。证明了该算法在离散形式下保持了原方程的质量和能量的守恒性，是无条件稳定的，收敛误差为O(h2+τ2)。最后通过数值实验验证了该算法的可行性和精度，说明该算法是一种简单有效的算法。
Abstract:
A timesplitting method for solving the fractional nonlinear Schrodinger equation with space fractional derivative was proposed.In this method,the fractional nonlinear Schrodinger equation was split into a linear equation and a nonlinear equation,where the nonlinear equation could be solved exactly and satisfy ‘conservation of point’,and the linear equation could be solved by using CrankNicolson discretization method.The conservation of mass and energy for the original equation was kept in this method.The unconditional stability and the convergence with the truncation error O(h2+τ2)were proved.Finally,numerical examples were presented to show that the method was both effective and accurate,which indicated that the method was simple and effective.

参考文献/References:

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相似文献/References:

[1]靳珊,梁宗旗.分数阶非线性Schrodinger方程的守恒算法[J].集美大学学报(自然科学版),2021,26(5):465.
　JIN Shan,LIANG Zongqi.A Conservative Method for the Fractional Nonlinear Schrodinger Equation[J].Journal of Jimei University,2021,26(1):465.

备注/Memo

备注/Memo:
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更新日期/Last Update: 2018-03-20