The Legendre Spectral-Collocation method for a class of fractional integral equations
For researchers working on numerical solutions of fractional integral equations, this method offers an efficient and accurate approach, though it is an incremental extension of existing spectral methods.
This paper presents a Legendre spectral-collocation method for solving fractional integral equations of the second kind, demonstrating exponential decay of the error in L^2 norm and validating accuracy through numerical comparisons with exact solutions.
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.