A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay

Abstract

In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with pantograph delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both $L^2$-norm and $L^∞$-norm.