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Zbl 1014.65143
Brunner, Hermann; Hu, Qiya; Lin, Qun
Geometric meshes in collocation methods for Volterra integral equations with proportional delays. (English)
[J] IMA J. Numer. Anal. 21, No.4, 783-798 (2001). ISSN 0272-4979; ISSN 1464-3642/e

The authors analyse the local superconvergence properties of iterated piecewise polynomial collocation solutions for linear second-kind Volterra integral equations with (vanishing) proportional delays. It is shown that on suitable geometric meshes collocation at the Gauss points leads to almost optimal superconvergence at the mesh points; in contrast with uniform meshes.\par The superconergence results are illustrated by a Volterra equation, which is solved by three collocation methods.
[Søren Christiansen (Lyngby)]

MSC 2000:: *65R20 Integral equations (numerical methods)
45D05 Volterra integral equations

Keywords: local superconvergence; linear second-kind Volterra integral equations; collocation methods

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