{"title":"Higher Order Stable Numerical Algorithm for the Variable Order Time-Fractional Sub-diffusion Equation","authors":"Priyanka Rajput, Nikhil Srivastava, Vineet Kumar Singh","doi":"10.1007/s40995-024-01726-5","DOIUrl":null,"url":null,"abstract":"<div><p>In the present work, we proposed a numerical scheme for solving the Variable order time fractional sub-diffusion equation (VOTFSDE) by finite difference method. The variable order Caputo derivative is approximated by the L-123 approximation in time direction. The numerical schemes unconditional stability is theoretically investigated. The three test problems are used to execute the scheme, and the numerical results show a high level of accuracy and higher order of convergence. To show the efficiency and accuracy of our proposed scheme, a comparison of the numerical results with those from an earlier existing scheme is also provided.</p></div>","PeriodicalId":600,"journal":{"name":"Iranian Journal of Science and Technology, Transactions A: Science","volume":"49 2","pages":"369 - 381"},"PeriodicalIF":1.4000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian Journal of Science and Technology, Transactions A: Science","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s40995-024-01726-5","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
In the present work, we proposed a numerical scheme for solving the Variable order time fractional sub-diffusion equation (VOTFSDE) by finite difference method. The variable order Caputo derivative is approximated by the L-123 approximation in time direction. The numerical schemes unconditional stability is theoretically investigated. The three test problems are used to execute the scheme, and the numerical results show a high level of accuracy and higher order of convergence. To show the efficiency and accuracy of our proposed scheme, a comparison of the numerical results with those from an earlier existing scheme is also provided.
期刊介绍:
The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences