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Spectral methods for weakly singular Volterra integral equations with pantograph delays

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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 L 2-norm. Numerical examples are presented to complement the theoretical convergence results.

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, China

    Ran Zhang & Benxi Zhu

  2. LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Hehu Xie

Authors
  1. Ran Zhang
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  2. Benxi Zhu
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  3. Hehu Xie
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Corresponding author

Correspondence to Benxi Zhu.

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Dedicated to Professor Hermann Brunner on his 70th birthday

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Zhang, R., Zhu, B. & Xie, H. Spectral methods for weakly singular Volterra integral equations with pantograph delays. Front. Math. China 8, 281–299 (2013). https://doi.org/10.1007/s11464-013-0282-1

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

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