[1]翟步祥,聂 涛*,薛 翔.5次非线性Schrdinger方程的一个线性化4层紧致差分格式[J].江西师范大学学报(自然科学版),2019,(01):35-38+51.[doi:10.16357/j.cnki.issn1000-5862.2019.01.07]
　ZHAI Buxiang,NIE Tao*,XUE Xiang.The Linearized Four-Level Compact Finite Difference Schemefor the Quintic Nonlinear Schrdinger Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2019,(01):35-38+51.[doi:10.16357/j.cnki.issn1000-5862.2019.01.07]
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5次非线性Schrödinger方程的一个线性化4层紧致差分格式()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2019年01期
页码:
35-38+51
栏目:
数学与应用数学
出版日期:
2019-02-10

文章信息/Info

Title:
The Linearized Four-Level Compact Finite Difference Scheme for the Quintic Nonlinear Schrödinger Equation
文章编号:
1000-5862(2019)01-0035-04
作者:
翟步祥1; 聂 涛1*; 薛 翔2
1.南京科技职业学院基础科学部,江苏 南京 210048; 2.南京信息工程大学数学与统计学院,江苏 南京 210044
Author(s):
ZHAI Buxiang1; NIE Tao1*; XUE Xiang2
1.Basic Department,Nanjing Polytechnic Institute,Nanjing Jiangsu 210048,China; 2.School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing Jiangsu 210044,China
关键词:
5次非线性Schrö; dinger方程;  紧致有限差分格式;  最优误差估计;  线性化4层格式;  计算效率
Keywords:
quintic nonlinear Schrö; dinger equation;  compact finite difference scheme;  optimal error estimate;  linearized four-level scheme;  computational efficiency
分类号:
O 241.8
DOI:
10.16357/j.cnki.issn1000-5862.2019.01.07
文献标志码:
A
摘要:
对5次非线性Schrödinger方程提出了一个线性化4层紧致有限差分格式,引入“抬升”技巧,运用标准的能量方法和数学归纳法建立了误差的最优估计,证明数值解在空间和时间2个方向分别具有4阶和2阶精度.数值实验对理论结果进行了验证,并通过对比表明该文格式在保持精度相当的前提下较已有格式具有更高的计算效率.
Abstract:
In this paper,a linearized four-level compact finite difference scheme for the nonlinear Schrödinger equation involving quintic term is proposed.By introducing a "lifting" technique,the optimal error estimate is established by using standard energy method and mathematical induction.It is proved that the numerical solution has fourth-order and second-order accuracy in space and in time,respectively.Numerical experiments are given to verify the theoretical results and compared with the existing results.The results show that the proposed scheme has higher computational efficiency under the condition of maintaining the accuracy.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-05-20
基金项目:国家自然科学基金(11571181)和江苏省自然科学基金(BK20171454)资助项目.
通信作者:聂 涛(1979-),女,山东青岛人,副教授,主要从事偏微分方程数值解的研究.E-mail:nietaonjcc@126.com
更新日期/Last Update: 2019-02-10