Barycentric Interpolation Collocation Method for Solving Fractional Linear Fredholm-Volterra Integro-Differential Equation

Abstract

In this article, barycentric interpolation collocation method (BICM) is presented to solve the fractional linear Fredholm-Volterra integro-differential equation (FVIDE). Firstly, the fractional order term of equation is transformed into the Riemann integral with Caputo definition, and this integral term is approximated by the Gauss quadrature formula. Secondly, the barycentric interpolation basis function is used to approximate the unknown function, and the matrix equation of BICM is obtained. Finally, several numerical examples are given to solve one-dimensional differential equation.