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Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays

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Abstract

The aims of this paper are (i) to present a survey of recent advances in the analysis of superconvergence of collocation solutions for linear Volterra-type functional integral and integro-differential equations with delay functions θ(t) vanishing at the initial point of the interval of integration (with ia(t) = qt (0 < q < 1, t ⩾ 0) being an important special case), and (ii) to point, by means of a list of open problems, to areas in the numerical analysis of such Volterra functional equations where more research needs to be carried out.

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

    Hermann Brunner

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

    Hermann Brunner

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  1. Hermann Brunner
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Brunner, H. Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays. Front. Math. China 4, 3–22 (2009). https://doi.org/10.1007/s11464-009-0001-0

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