Analysis of collocation methods for generalized auto-convolution volterra integral equations

Ran Zhang, Hui Liang, Hermann BRUNNER

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We first study the existence, uniqueness, and regularity properties of solutions to a generalized version of the auto-convolution Volterra integral equation of the second kind. These results are then used to establish the optimal global and local (super) convergence properties of piecewise polynomial collocation solutions for such integral equations. The theoretical results are illustrated by extensive numerical examples.

Original languageEnglish
Pages (from-to)899-920
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number2
DOIs
Publication statusPublished - 2016

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Auto-convolution volterra integral equations
  • Collocation methods
  • Existence and regularity of solutions
  • Optimal order of convergence
  • Superconvergence

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