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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  and
Yanping Chen
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:yunxiawei@126.com
Corresponding author.Email address:yanpingchen@scnu.edu.cn
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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.

Keywords

45L1065R2065D15Second order Volterra integro-differential equationsGauss quadrature formulaLegendre-collocation methodsconvergence analysis
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 3 , August 2011 , pp. 419 - 438
Copyright
Copyright © Global Science Press Limited 2011

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