Piecewise barycentric interpolating functions for the numerical solution of Volterra integro‐differential equations

Abstract

This investigation presents an effective numerical scheme using a new set of basis functions, namely, the piecewise barycentric interpolating functions, to find the approximate solution of Volterra integro-differential equations (VIDEs).The operational matrices of integration and product for the PBIFs are provided. Then these operational matrices are utilized to reduce the VIDEs to a system of algebraic equations. Applying the Floater-Hormann weights, the convergence analysis of the PBIFs method is studied. Finally, several numerical examples are provided to illustrate the efficiency and validity of the proposed method in acceptable computational times, and the results are compared with some existing numerical methods. KEYWORDS convergence analysis, Floater-Hormann interpolant, operational matrices of integral and product, piecewise barycentric interpolating functions, Volterra integro-differential equations MSC CLASSIFICATION 45D05; 45G10; 65R20; 65D05