Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Integral-algebraic equations: Theory of collocation methods I

Language

English

Abstract

Our analysis of collocation solutions for general systems of linear integral-algebraic equations (IAEs) is based on the notions of the tractability index and the ν-smoothing property of a Volterra integral operator. These are used to decouple the given IAE system into the inherent system of regular second-kind Volterra integral equations (VIEs) and a system of first-kind VIEs. This decoupling is then used to derive the optimal convergence properties of piecewise polynomial collocation solutions. Numerical examples illustrate the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Keywords

ν-smoothing Volterra operator, Collocation solutions, Index-μ tractability, Integral-algebraic equations, Optimal order of convergence, Tractability index

Publication Date

2013

Source Publication Title

SIAM Journal on Numerical Analysis

Volume

51

Issue

4

Start Page

2238

End Page

2259

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/120894567

Link to Publisher's Edition

http://dx.doi.org/10.1137/120894567

ISSN (print)

00361429

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