{"title":"Conservative Crank–Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity","authors":"Yong Wu , Fenghua Tong , Xuanxuan Zhou , 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.
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.