The convergence of collocation solutions in continuous piecewise polynomial spaces for weakly singular volterra integral equations

Hui Liang, Hermann BRUNNER

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Collocation solutions by globally continuous piecewise polynomials to second-kind Volterra integral equations (VIEs) with smooth kernels are uniformly convergent only for certain sets of collocation points. In this paper we establish the analogous convergence theory for VIEs with weakly singular kernels, for both uniform and graded meshes.

Original languageEnglish
Pages (from-to)1875-1896
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume57
Issue number4
DOIs
Publication statusPublished - 2019

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Collocation solutions
  • Globally continuous piecewise polynomials
  • Uniform convergence
  • Volterra integral equations
  • Weakly singular kernels

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