{"title":"Efficient mapped Jacobi spectral method for integral equations with two-sided singularities","authors":"Xiu Yang , Changtao Sheng","doi":"10.1016/j.apnum.2024.08.003","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we develop a mapped Jacobi spectral Galerkin method for solving the multi-term Fredholm integral equations (MFIEs) with two-sided weakly singularities. We introduce a new family of mapped Jacobi functions (MJFs) and establish the corresponding spectral approximation results on these MJFs in weighted Sobolev spaces involving the mapped Jacobi weight function. These MJFs serve as the basis functions in our algorithm design and are tailored to the two-sided end-points singularities of the solution by using suitable mapping. Moreover, we derive the error estimates of the proposed method for MFIEs. Finally, the numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"206 ","pages":"Pages 94-110"},"PeriodicalIF":2.2000,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424001995","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 develop a mapped Jacobi spectral Galerkin method for solving the multi-term Fredholm integral equations (MFIEs) with two-sided weakly singularities. We introduce a new family of mapped Jacobi functions (MJFs) and establish the corresponding spectral approximation results on these MJFs in weighted Sobolev spaces involving the mapped Jacobi weight function. These MJFs serve as the basis functions in our algorithm design and are tailored to the two-sided end-points singularities of the solution by using suitable mapping. Moreover, we derive the error estimates of the proposed method for MFIEs. Finally, the numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method.
IF 6.3 4区 医学Systematic ReviewsPub Date : 2022-10-26DOI: 10.1186/s13643-022-02099-9
Alexandria Bennett, Andrew Beck, Nicole Shaver, Roland Grad, Allana LeBlanc, Heather Limburg, Casey Gray, Ahmed Abou-Setta, Scott Klarenbach, Navindra Persaud, Guylène Thériault, Brett D Thombs, Keith J Todd, Neil Bell, Philipp Dahm, Andrew Loblaw, Lisa Del Giudice, Xiaomei Yao, Becky Skidmore, Elizabeth Rolland-Harris, Melissa Brouwers, Julian Little, David Moher
IF 0 medRxiv - OncologyPub Date : 2024-05-31DOI: 10.1101/2024.05.29.24308154
Alexandria Bennett, Nicole Shaver, Niyati Vyas, Faris Almoli, Robert Pap, Andrea Douglas, Taddele Kibret, Becky Skidmore, Martin Yaffe, Anna Wilkinson, Jean M. Seely, Julian Little, David Moher
期刊介绍:
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.