{"title":"Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity","authors":"Rui-lian Du, Zhi-zhong Sun","doi":"10.1007/s10255-024-1054-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, a novel time-stepping <span>\\(\\overline{L1}\\)</span> formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity. This formula can obtain second-order accuracy and an error estimate is analyzed strictly. As an application, a fully discrete difference scheme is established for the initial-boundary value problem of a hidden-memory variable-order time fractional diffusion model. Numerical experiments are provided to support our theoretical results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1060 - 1077"},"PeriodicalIF":0.9000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-024-1054-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, a novel time-stepping \(\overline{L1}\) formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity. This formula can obtain second-order accuracy and an error estimate is analyzed strictly. As an application, a fully discrete difference scheme is established for the initial-boundary value problem of a hidden-memory variable-order time fractional diffusion model. Numerical experiments are provided to support our theoretical results.
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.