Journal of Scientific Computing

, Volume 53, Issue 3, pp 672–688

# Legendre Spectral Collocation Methods for Pantograph Volterra Delay-Integro-Differential Equations

• Yunxia Wei
• Yanping Chen
Article

## Abstract

This paper is concerned with the convergence properties of the Legendre spectral collocation methods when used to approximate smooth solutions of Volterra integro-differential equations with proportional (vanishing) delays. We provide a vigorous error analysis for the proposed methods. Furthermore, we prove that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in L 2-norm and L -norm. Some numerical experiments are given to confirm the theoretical results.

## Keywords

Volterra delay-integro-differential equations Legendre-collocation methods Gauss quadrature formula Convergence analysis

## Notes

### Acknowledgements

This work is supported by the Foundation for Talent Introduction of Guangdong Provincial University, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2008), National Science Foundation of China (10971074).

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