Conservative Crank–Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Yong Wu , Fenghua Tong , Xuanxuan Zhou , Yongyong Cai
{"title":"Conservative Crank–Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity","authors":"Yong Wu ,&nbsp;Fenghua Tong ,&nbsp;Xuanxuan Zhou ,&nbsp;Yongyong Cai","doi":"10.1016/j.aml.2025.109553","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we propose conservative Crank–Nicolson-type and compact finite difference schemes for the nonlinear Schrödinger equation with point nonlinearity. To construct these schemes, we first transform the point nonlinearity into an interface condition, then decompose the computational domain along the interface into two subregions with a jump condition. Different discretization approximations of the jump condition lead to different numerical schemes. For the Crank–Nicolson finite difference scheme, we prove its unconditional mass conservation and energy conservation. Some numerical examples are also presented to illustrate the accuracy and efficiency of our proposed schemes.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109553"},"PeriodicalIF":2.9000,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S089396592500103X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, we propose conservative Crank–Nicolson-type and compact finite difference schemes for the nonlinear Schrödinger equation with point nonlinearity. To construct these schemes, we first transform the point nonlinearity into an interface condition, then decompose the computational domain along the interface into two subregions with a jump condition. Different discretization approximations of the jump condition lead to different numerical schemes. For the Crank–Nicolson finite difference scheme, we prove its unconditional mass conservation and energy conservation. Some numerical examples are also presented to illustrate the accuracy and efficiency of our proposed schemes.
具有点非线性的Schrödinger方程的保守crank - nicolson型和紧致有限差分格式
本文给出了具有点非线性的非线性Schrödinger方程的保守的crank - nicolson型有限差分格式和紧致有限差分格式。为了构造这些格式,我们首先将点非线性转化为一个界面条件,然后将沿界面的计算域分解为两个具有跳跃条件的子区域。不同的跃变条件离散化近似导致不同的数值格式。对于Crank-Nicolson有限差分格式,我们证明了它的无条件质量守恒和能量守恒。数值算例说明了所提方法的准确性和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
期刊介绍: The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信