Collocation methods based on barycentric rational interpolation for Volterra integro‐differential equations with weakly singular kernels

Abstract

This paper is concerned with the numerical solution of Volterra integro‐differential equations with weakly singular kernels. A smoothing transformation is first used to convert the original equation to a new equation with better regularity. A collocation method based on barycentric rational interpolation is introduced. The convergence and supercovergence of the numerical solution are studied in detail. Some numerical results are illustrated to confirm the theoretical prediction of the rate of convergence and superconvergence.