A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations
Qingqing Wu , Zhongshu Wu , Xiaoyan Zeng
Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (3) : 509 -526.
A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations
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.
National Natural Science Foundation of China(11701358)
National Natural Science Foundation of China(11774218)
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