A quadrature method for Volterra integral equations of the first kind

This paper introduces a direct quadrature method for the numerical solution of Volterra integral equations of the first kind, utilizing a composite quadrature scheme based on the Floater–Hormann family of linear barycentric rational interpolants. The convergence of the proposed method is rigorously proved, and the order of convergence is explicitly derived in terms of the parameters of the method, thereby providing a clear theoretical framework for its performance. Several numerical experiments are provided to demonstrate both the efficiency and accuracy of the method, as well as to verify the excellent agreement between the implementation results and the theoretically predicted convergence rates.