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

Published online by Cambridge University Press:  28 May 2015

Yunxia Wei*
Affiliation:
School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
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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-norm and L2-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

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