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13 Feb 2009
Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays
 Hermann Brunner
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The aims of this paper are (i) to present a survey of recent advances in the analysis of superconvergence of collocation solutions for linear Volterratype functional integral and integrodifferential 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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 Title
 Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays
 Journal

Frontiers of Mathematics in China
Volume 4, Issue 1 , pp 322
 Cover Date
 20090301
 DOI
 10.1007/s1146400900010
 Print ISSN
 16733452
 Online ISSN
 16733576
 Publisher
 SP Higher Education Press
 Additional Links
 Topics
 Keywords

 Volterra functional integral and integrodifferential equation
 vanishing delay
 pantograph equation
 collocation solution
 optimal order of superconvergence
 65R20
 34K06
 34K28
 Authors

 Hermann Brunner ^{(1)} ^{(2)}
 Author Affiliations

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