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

Hui Liang*, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)359-391
Number of pages33
JournalJournal of Integral Equations and Applications
Issue number3
Publication statusPublished - 2012

Scopus Subject Areas

  • Numerical Analysis
  • Applied Mathematics

User-Defined Keywords

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


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