Abstract
The aim of this paper is to obtain the numerical solutions of fractional Volterra integro-differential 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 \(L^{\infty }\) norm. Two numerical examples demonstrate the high accuracy and fast convergence of the method at last.
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Acknowledgements
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.
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Wu, Q., Wu, Z. & Zeng, X. A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations. Commun. Appl. Math. Comput. 3, 509–526 (2021). https://doi.org/10.1007/s42967-020-00099-x
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DOI: https://doi.org/10.1007/s42967-020-00099-x
Keywords
- Fractional integro-differential equation
- Caputo fractional derivative
- Jacobi spectral collocation method
- Convergence analysis