Analysis of collocation solutions for a class of functional equations with vanishing delays

Hermann BRUNNER*, Hehu Xie, Ran Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

We study the existence, uniqueness and regularity properties of solutions for the functional equation y(t) = b(t)y(θ(t)) + f(t), t ∈ [0, T], where the delay function θ(t) vanishes at t = 0. Functional equations corresponding to the linear delay function θ(t) = qt (0 < q < 1) represent an important special case. We then analyse the optimal order of convergence of piecewise polynomial collocation approximations to solutions of these functional equations. The theoretical results are illustrated by extensive numerical examples.

Original languageEnglish
Pages (from-to)698-718
Number of pages21
JournalIMA Journal of Numerical Analysis
Volume31
Issue number2
DOIs
Publication statusPublished - Apr 2011

Scopus Subject Areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • collocation solutions
  • functional equation with vanishing delay
  • integro-functional equation
  • optimal order of convergence
  • q-difference equation
  • uniqueness and regularity of solution

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