http://dx.doi.org/10.1216/JIE-2012-24-3-359">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Discrete superconvergence of collocation solutions for first-kind volterra integral equations

Language

English

Abstract

It is known that collocation solutions for firstkind Volterra integral equations based on (discontinuous or continuous) piecewise polynomials cannot exhibit local superconvergence at the points of a uniform mesh. In this paper we present a complete analysis of local superconvergence of such collocation solutions for first-kind Volterra integral equations at non-mesh points. In particular, we discuss (i) the existence of superconvergence points for prescribed collocation points; (ii) the existence of collocation points for prescribed superconvergence points. Numerous examples illustrate the theory. © 2012 Rocky Mountain Mathematics Consortium.

Keywords

Collocation solutions, First-kind volterra integral equations, Piecewise polynomials, Superconvergence at non-mesh points

Publication Date

2012

Source Publication Title

Journal of Integral Equations and Applications

Volume

24

Issue

3

Start Page

359

End Page

391

Publisher

Rocky Mountain Mathematics Conso

ISSN (print)

08973962

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