Collocation methods for general volterra functional integral equations with vanishing delays

Hehu Xie*, Ran Zhang, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

We analyze the existence, uniqueness, and regularity properties of solutions for general Volterra functional integral equations with the delay function θ(t) vanishing at the initial point of the given interval [0, T] (with θ(t) = qt, 0 > q > 1, representing an important special case). The focus of the paper is then on the the attainable order of convergence, and the question of possible superconvergence, for collocation solutions in certain piecewise polynomial spaces. Numerical experiments complement the theoretical convergence results.

Original languageEnglish
Pages (from-to)3303-3332
Number of pages30
JournalSIAM Journal of Scientific Computing
Volume33
Issue number6
DOIs
Publication statusPublished - 2011

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Collocation solutions
  • Existence and regularity of solutions
  • Optimal order of convergence
  • Pantograph-type delays
  • Vanishing delays
  • Volterra functional integral equations

Fingerprint

Dive into the research topics of 'Collocation methods for general volterra functional integral equations with vanishing delays'. Together they form a unique fingerprint.

Cite this