Chelyshkov collocation approach for solving linear weakly singular Volterra integral equations

Abstract

The purpose of this paper is to present a new numerical algorithm for solving the weakly singular Volterra integral equations. The operational matrix of fractional integral based on fractional-order Chelyshkov polynomials is constructed and together with the collocation method is used to reduce the integral equation into a system of algebraic equations. The convergence of the method is discussed in $$L^{2}$$ -norm and finally, some numerical examples are shown to illustrate the accuracy of the proposed method.