The Legendre Spectral-Collocation method for a class of fractional integral equations

TL;DR

This paper introduces a spectral-collocation method based on Legendre-Gauss-Lobatto points for efficiently solving fractional integral equations of the second kind, demonstrating exponential error decay and high accuracy.

Contribution

The paper develops a novel spectral-collocation approach using Legendre-Gauss-Lobatto points specifically for fractional integral equations of the second kind, with proven exponential error decay.

Findings

Method is efficient and accurate for fractional integral equations.

Numerical results agree with exact solutions.

Error decays exponentially in L^2 norm.

Abstract

In this paper, we consider spectral-collocation method base on Legendre-Gauss-Lobatto point. We present a computational method for solving a class of fractional integral equation of the second kind. Then based on Legendre-Gauss-Lobatto point and using, we derive a system of algebraic equations. The method is illustrated by applications and the results obtained are compared with the exact solutions in open literature. The obtained numerical results show that our proposed method is efficient and accurate for fractional integral equations of second kind. In addition, we prove that the error of the approximate solution decay exponentially in L^2 norm.