Frontiers of Mathematics in China >

2013 , Vol. 8 >Issue 2: 281 - 299

DOI: https://doi.org/10.1007/s11464-013-0282-1

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Spectral methods for weakly singular Volterra integral equations with pantograph delays

  • Ran ZHANG 1 ,
  • Benxi ZHU , 1 ,
  • Hehu XIE 2
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  • 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

Received date: 30 Mar 2012

Accepted date: 22 Apr 2012

Published date: 01 Apr 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Volterra integral equation; vanishing delay; weakly singular kernel; Jacobi-spectral collocation method; error analysis

Cite this article

Ran ZHANG , Benxi ZHU , Hehu XIE . Spectral methods for weakly singular Volterra integral equations with pantograph delays[J]. Frontiers of Mathematics in China, 2013 , 8(2) : 281 -299 . DOI: 10.1007/s11464-013-0282-1

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