Legendre Spectral Collocation Methods for Pantograph Volterra Delay-Integro-Differential Equations

Abstract

This paper is concerned with the convergence properties of the Legendre spectral collocation methods when used to approximate smooth solutions of Volterra integro-differential equations with proportional (vanishing) delays. We provide a vigorous error analysis for the proposed methods. Furthermore, we prove that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in L 2-norm and L ?-norm. Some numerical experiments are given to confirm the theoretical results.