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

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.

Keywords

• fractional integro-differential equations
• numerical algorithm
• shifted legendre polynomials
• error analysis