A class of reducible quadrature rules for the second-kind Volterra integral equations using barycentric rational interpolation

Abstract

Reducible quadrature rules constitute a well-established class of direct quadrature methods for approximating solutions to Volterra integral equations. Unlike interpolatory quadrature formulae, the reducible quadrature rule can be constructed without the need for additional calculations of moments. This paper investigates the reducible quadrature rule by employing barycentric rational interpolation to solve the underlying initial value problem and analyzes its convergence and stability. It is found that these quadrature rules exhibit high-order convergence rates accompanied by extensive stability regions. Several numerical illustrations are provided to verify the theoretical results.