{"title":"Numerical Study of Time-Fractional Telegraph Equations of Transmission Line Modeling","authors":"Wang Kong, Zhongyi Huang","doi":"10.4208/eajam.070921.150222","DOIUrl":null,"url":null,"abstract":". The stability and uniqueness of the solutions of time-fractional telegraph equations arising in the transmission line modeling are proved. The corresponding initial-boundary problems are then solved by a finite difference scheme. It is shown that the scheme is unconditionally stable and convergent. Computational efficiency of the method can be enhanced by transforming it into two finite volume schemes for solving two uncoupled time-fractional convection equations. Numerical experiments validate the theoretical results and show the efficiency of this approach even for the problems the solutions which are not smooth at the initial moment.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"East Asian Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/eajam.070921.150222","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
. The stability and uniqueness of the solutions of time-fractional telegraph equations arising in the transmission line modeling are proved. The corresponding initial-boundary problems are then solved by a finite difference scheme. It is shown that the scheme is unconditionally stable and convergent. Computational efficiency of the method can be enhanced by transforming it into two finite volume schemes for solving two uncoupled time-fractional convection equations. Numerical experiments validate the theoretical results and show the efficiency of this approach even for the problems the solutions which are not smooth at the initial moment.
期刊介绍:
The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.