Integral-Algebraic Equations: Theory of Collocation Methods I

Hui Liang, Hermann Brunner

Research output: Contribution to journalJournal articlepeer-review

32 Citations (Scopus)
16 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)2238-2259
Number of pages22
JournalSIAM Journal on Numerical Analysis
Issue number4
Publication statusPublished - 1 Aug 2013

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

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


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