Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations

Abstract

A class of numerical methods is developed for second order Volterra integro-differential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the $L^\infty$-norm and $L^2$-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods.