On the stability preserving of L1 scheme to nonlinear time-fractional Schrödinger delay equations

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2024-12-13 DOI:10.1016/j.matcom.2024.11.020

Zichen Yao, Zhanwen Yang, Lixin Cheng

{"title":"On the stability preserving of L1 scheme to nonlinear time-fractional Schrödinger delay equations","authors":"Zichen Yao, Zhanwen Yang, Lixin Cheng","doi":"10.1016/j.matcom.2024.11.020","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate the stability preserving of L1 scheme to nonlinear time fractional Schrödinger delay equations. This kind of Schrödinger equation contains both nonlocal effect and time memory reaction term. We derive sufficient conditions to ensure the asymptotic stability of the analytical equations. After that, we approximate the equations via the Galerkin finite element method in space. We show that the semidiscrete numerical solutions can inherit the long time behavior of the solutions. After that, a fully discrete approximation of the equations is obtained by the L1 scheme and a linear interpolation procedure. We provide detailed estimations on the discrete operators that are obtained by the Z transform and its inverse. Together with a discrete fractional comparison principle, we prove that the L1 scheme preserves the stability of the underlying equations. The main results obtained in this work do not depend on spatial and temporal step sizes. A numerical example confirms the effectiveness of our derived method and validates the theoretical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"231 ","pages":"Pages 209-220"},"PeriodicalIF":4.4000,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378475424004695","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

In this paper, we investigate the stability preserving of L1 scheme to nonlinear time fractional Schrödinger delay equations. This kind of Schrödinger equation contains both nonlocal effect and time memory reaction term. We derive sufficient conditions to ensure the asymptotic stability of the analytical equations. After that, we approximate the equations via the Galerkin finite element method in space. We show that the semidiscrete numerical solutions can inherit the long time behavior of the solutions. After that, a fully discrete approximation of the equations is obtained by the L1 scheme and a linear interpolation procedure. We provide detailed estimations on the discrete operators that are obtained by the Z transform and its inverse. Together with a discrete fractional comparison principle, we prove that the L1 scheme preserves the stability of the underlying equations. The main results obtained in this work do not depend on spatial and temporal step sizes. A numerical example confirms the effectiveness of our derived method and validates the theoretical findings.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.