The barycentric rational predictor-corrector schemes for Volterra integral equations

Abstract

This paper introduces a family of barycentric rational predictor-corrector schemes based on the Floater–Hormann family of linear barycentric rational interpolants (LBRIs) for the numerical solution of classical systems of second-kind Volterra integral equations. Also, we introduce a family of LBRI-based predictor-corrector starting procedures that is essentially explicit and whose order of convergence can be as high as that of the main method. Numerical tests verify the theoretical results on the convergence order and stability and illustrate the efficiency and power of the developed family of methods in solving stiff equations.