一类分数初值问题的中心部分插值格式

IF 0.3 Q4 MATHEMATICS

Acta et Commentationes Universitatis Tartuensis de Mathematica Pub Date : 2022-05-27 DOI:10.12697/acutm.2022.26.11

M. Vikerpuur, Margus Lillemäe, A. Pedas

{"title":"一类分数初值问题的中心部分插值格式","authors":"M. Vikerpuur, Margus Lillemäe, A. Pedas","doi":"10.12697/acutm.2022.26.11","DOIUrl":null,"url":null,"abstract":"We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"55 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Central part interpolation schemes for a class of fractional initial value problems\",\"authors\":\"M. Vikerpuur, Margus Lillemäe, A. Pedas\",\"doi\":\"10.12697/acutm.2022.26.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.\",\"PeriodicalId\":42426,\"journal\":{\"name\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"volume\":\"55 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12697/acutm.2022.26.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta et Commentationes Universitatis Tartuensis de Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12697/acutm.2022.26.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

研究一类具有弱奇异核的线性分数阶积分微分方程的初值问题。通过对底层问题的积分方程重新表述，构造并分析了均匀网格上基于连续分段多项式中心部分插值的配置方法。通过数值实验验证了该方法的最优收敛阶。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Central part interpolation schemes for a class of fractional initial value problems

We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta et Commentationes Universitatis Tartuensis de Mathematica MATHEMATICS-

CiteScore

0.60

自引率

33.30%

发文量