A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations

doi:10.1007/s42967-020-00099-x

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (3): 509-526.doi: 10.1007/s42967-020-00099-x

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A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations

Qingqing Wu, Zhongshu Wu, Xiaoyan Zeng

Department of Mathematics, Shanghai University, Shanghai 200444, China

收稿日期:2020-05-22 修回日期:2020-08-06 出版日期:2021-09-20 发布日期:2021-09-16
通讯作者: Xiaoyan Zeng E-mail:cherryzxy@shu.edu.cn
基金资助:
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11701358, 11774218). The authors wish to thank Professor Heping Ma and Professor Changpin Li for their valuable discussions.

A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations

Qingqing Wu, Zhongshu Wu, Xiaoyan Zeng

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received:2020-05-22 Revised:2020-08-06 Online:2021-09-20 Published:2021-09-16
Contact: Xiaoyan Zeng E-mail:cherryzxy@shu.edu.cn
Supported by:
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11701358, 11774218). The authors wish to thank Professor Heping Ma and Professor Changpin Li for their valuable discussions.

摘要/Abstract

摘要： The aim of this paper is to obtain the numerical solutions of fractional Volterra integrodifferential equations by the Jacobi spectral collocation method using the Jacobi-Gauss collocation points. We convert the fractional order integro-differential equation into integral equation by fractional order integral, and transfer the integro equations into a system of linear equations by the Gausssian quadrature. We furthermore perform the convergence analysis and prove the spectral accuracy of the proposed method in L^∞ norm. Two numerical examples demonstrate the high accuracy and fast convergence of the method at last.

关键词: Fractional integro-differential equation, Caputo fractional derivative, Jacobi spectral collocation method, Convergence analysis

Abstract: The aim of this paper is to obtain the numerical solutions of fractional Volterra integrodifferential equations by the Jacobi spectral collocation method using the Jacobi-Gauss collocation points. We convert the fractional order integro-differential equation into integral equation by fractional order integral, and transfer the integro equations into a system of linear equations by the Gausssian quadrature. We furthermore perform the convergence analysis and prove the spectral accuracy of the proposed method in L^∞ norm. Two numerical examples demonstrate the high accuracy and fast convergence of the method at last.

Key words: Fractional integro-differential equation, Caputo fractional derivative, Jacobi spectral collocation method, Convergence analysis

中图分类号:

65M70
35R11

Qingqing Wu, Zhongshu Wu, Xiaoyan Zeng. A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations[J]. Communications on Applied Mathematics and Computation, 2021, 3(3): 509-526.

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A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations

A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations

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