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

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.

Funding

National Natural Science Foundation of China(11701358); National Natural Science Foundation of China(11774218)