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

Chuanhua Wu; Ziqiang Wang; Chuanhua Wu; Ziqiang Wang

doi:10.3934/math.2022532

AIMS Mathematics

2022, Volume 7, Issue 6: 9577-9587. doi: 10.3934/math.2022532

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Research article

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

Chuanhua Wu ,
Ziqiang Wang ^,

School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China

Received: 07 September 2021 Revised: 26 February 2022 Accepted: 07 March 2022 Published: 14 March 2022
MSC : 26A33, 65M15, 65M70

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.
- fractional integro-differential equations,
- numerical algorithm,
- shifted Legendre polynomials,
- error analysis
Citation: Chuanhua Wu, Ziqiang Wang. The spectral collocation method for solving a fractional integro-differential equation[J]. AIMS Mathematics, 2022, 7(6): 9577-9587. doi: 10.3934/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.

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