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Stability of collocation methods for delay differential equations with vanishing delays

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Abstract

We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0<q<1) (pantograph DDEs). It is shown that if the collocation points are such that the analogous collocation solution for ODEs is A-stable, then this asymptotic behaviour is inherited by the collocation solution for the pantograph DDE.

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Authors and Affiliations

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

    Hermann Brunner

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China

    Hermann Brunner

  3. School of Mathematical Sciences, Heilongjiang University, Harbin, Heilongjiang, China

    Hui Liang

Authors
  1. Hermann Brunner
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  2. Hui Liang
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Correspondence to Hermann Brunner.

Additional information

Communicated by Timo Eirola.

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Brunner, H., Liang, H. Stability of collocation methods for delay differential equations with vanishing delays. Bit Numer Math 50, 693–711 (2010). https://doi.org/10.1007/s10543-010-0285-1

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  • DOI: https://doi.org/10.1007/s10543-010-0285-1

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