Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations

Abstract

For their high accuracy and good stability properties, implicit numerical methods are widely used for solving Volterra integral equations, while, in order to save computational effort, explicit algorithms are preferred in the case of non-stiff problems. In this paper, highly accurate explicit methods based on the Floater–Hormann family of linear barycentric rational interpolants are presented. The order of convergence is obtained in terms of the parameters of the methods. Moreover, the linear stability properties with respect to both the basic and convolution test equations are analyzed in detail. Numerical experiments are discussed in order to validate the theoretical results and illustrate the efficiency and power of the methods applied to non-stiff and mildly stiff problems.