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 integrodifferential 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∞-norm and L 2-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods. © 2011 Global-Science Press.