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Spectral methods for pantograph-type differential and integral equations with multiple delays

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Abstract

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.

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Authors and Affiliations

  1. Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Ishtiaq Ali

  2. Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan

    Ishtiaq Ali

  3. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Newfoundland, Canada

    Hermann Brunner

  4. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

    Hermann Brunner & Tao Tang

Authors
  1. Ishtiaq Ali
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  2. Hermann Brunner
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  3. Tao Tang
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Correspondence to Ishtiaq Ali.

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Ali, I., Brunner, H. & Tang, T. Spectral methods for pantograph-type differential and integral equations with multiple delays. Front. Math. China 4, 49–61 (2009). https://doi.org/10.1007/s11464-009-0010-z

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  • DOI: https://doi.org/10.1007/s11464-009-0010-z

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