The spectral collocation method for solving a fractional integro-differential equation

In this paper, we propose a high-precision numerical algorithm for a fractional integro-differential equation based on the shifted Legendre polynomials and the idea of Gauss-Legendre quadrature rule and spectral collocation method. The error analysis of this method is also given in detail. Some nume...

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Published inAIMS mathematics Vol. 7; no. 6; pp. 9577 - 9587
Main Authors Wu, Chuanhua, Wang, Ziqiang
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
error analysis
fractional integro-differential equations
numerical algorithm
shifted legendre polynomials
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022532

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Abstract In this paper, we propose a high-precision numerical algorithm for a fractional integro-differential equation based on the shifted Legendre polynomials and the idea of Gauss-Legendre quadrature rule and spectral collocation method. The error analysis of this method is also given in detail. Some numerical examples are give to illustrate the exponential convergence of our method.
AbstractList In this paper, we propose a high-precision numerical algorithm for a fractional integro-differential equation based on the shifted Legendre polynomials and the idea of Gauss-Legendre quadrature rule and spectral collocation method. The error analysis of this method is also given in detail. Some numerical examples are give to illustrate the exponential convergence of our method.
Author Wang, Ziqiang
Wu, Chuanhua
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Cites_doi 10.4208/nmtma.OA-2020-0039
10.1080/00207160310001650044
10.1080/00207160701242300
10.1016/j.cam.2013.07.050
10.1016/j.amc.2005.09.059
10.1007/s11071-012-0547-3
10.1016/j.aej.2021.09.053
10.1016/j.sigpro.2014.10.002
10.4208/cicp.020709.221209a
10.1016/j.amc.2006.10.001
10.1007/s10958-012-0811-6
10.1080/00207160.2019.1673892
10.1155/2019/3734617
10.1016/j.cam.2017.02.027
10.1016/j.physleta.2005.05.045
10.1080/00207160.2020.1796985
10.4208/aamm.2013.m333
10.1007/s11425-014-4831-1
10.1016/j.amc.2018.05.017
10.1007/s10915-015-0069-5
10.1016/j.matcom.2022.01.012
10.1016/j.amc.2014.07.050
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SubjectTerms error analysis
fractional integro-differential equations
numerical algorithm
shifted legendre polynomials
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