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Frontiers of Mathematics in China

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ISSN 1673-3576(Online)

CN 11-5739/O1

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Front Math Chin    2013, Vol. 8 Issue (2) : 281-299    https://doi.org/10.1007/s11464-013-0282-1
REVIEW ARTICLE
Spectral methods for weakly singular Volterra integral equations with pantograph delays
Ran ZHANG1, Benxi ZHU1(), Hehu XIE2
1. School of Mathematics, Jilin University, Changchun 130012, China; 2. LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
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Abstract

In this paper, the convergence analysis of the Volterra integral equation of second kind with weakly singular kernel and pantograph delays is provided. We use some function transformations and variable transformations to change the equation into a new Volterra integral equation with pantograph delays defined on the interval [-1, 1], so that the Jacobi orthogonal polynomial theory can be applied conveniently. We provide a rigorous error analysis for the proposed method in the L∞-norm and the weighted L2-norm. Numerical examples are presented to complement the theoretical convergence results.
Keywords Volterra integral equation      vanishing delay      weakly singular kernel      Jacobi-spectral collocation method      error analysis     
Corresponding Author(s): ZHU Benxi,Email:zhubx@jlu.edu.cn   
Issue Date: 01 April 2013
 Cite this article:   
Ran ZHANG,Benxi ZHU,Hehu XIE. Spectral methods for weakly singular Volterra integral equations with pantograph delays[J]. Front Math Chin, 2013, 8(2): 281-299.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-013-0282-1
https://academic.hep.com.cn/fmc/EN/Y2013/V8/I2/281
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