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Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels

Part of:Partial differential equations, initial value and time-dependent initial-boundary value problemsVolterra integral equationsIntegral equations, integral transforms

Published online by Cambridge University Press:  27 May 2016

Xiulian Shi and
Yanping Chen
Xiulian Shi*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaSchool of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
*
*Corresponding author. Email:pgny@163.com (X. L. Shi), yanpingchen@scnu.edu.cn (Y. P. Chen)
*Corresponding author. Email:pgny@163.com (X. L. Shi), yanpingchen@scnu.edu.cn (Y. P. Chen)

Abstract

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A spectral Jacobi-collocation approximation is proposed for Volterra delay integro-differential equations with weakly singular kernels. In this paper, we consider the special case that the underlying solutions of equations are sufficiently smooth. We provide a rigorous error analysis for the proposed method, which shows that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in L∞ norm and weighted L2 norm. Finally, two numerical examples are presented to demonstrate our error analysis.

Keywords

Volterra integro-differential equationsspectral Jacobi-collocation methodpantograph delayweakly singular kernel

MSC classification

Secondary:65R20: Integral equations65M70: Spectral, collocation and related methods45D05: Volterra integral equations

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 4 , August 2016, pp. 648 - 669
Copyright
Copyright © Global-Science Press 2016 

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