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BIT Numerical Mathematics

, Volume 44, Issue 4, pp 631–650 | Cite as

On the Divergence of Collocation Solutions in Smooth Piecewise Polynomial Spaces for Volterra Integral Equations

  • Hermann Brunner
Article

Abstract

In this paper we present a characterization of those smooth piecewise polynomial collocation spaces that lead to divergent collocation solutions for Volterra integral equations of the second kind. The key to these results is an equivalence result between such collocation solutions and collocation solutions in slightly smoother spaces for initial-value problems for ordinary differential equations. For the latter problems Mülthei (1979/1980) established a complete divergence (and convergence) theory. Our analysis can be extended to furnish divergence results for smooth collocation solutions to Volterra integral equations of the first kind.

Keywords

Volterra integral equations collocation methods smooth piecewise polynomial spaces divergence of collocation solutions 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Dept. of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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