Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays

Hermann BRUNNER*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

The aims of this paper are (i) to present a survey of recent advances in the analysis of superconvergence of collocation solutions for linear Volterra-type functional integral and integro-differential equations with delay functions θ(t) vanishing at the initial point of the interval of integration (with ia(t) = qt (0 < q < 1, t ≥ 0) being an important special case), and (ii) to point, by means of a list of open problems, to areas in the numerical analysis of such Volterra functional equations where more research needs to be carried out.

Original languageEnglish
Pages (from-to)3-22
Number of pages20
JournalFrontiers of Mathematics in China
Volume4
Issue number1
DOIs
Publication statusPublished - Mar 2009

Scopus Subject Areas

  • Mathematics (miscellaneous)

User-Defined Keywords

  • Collocation solution
  • Optimal order of superconvergence
  • Pantograph equation
  • Vanishing delay
  • Volterra functional integral and integro-differential equation

Fingerprint

Dive into the research topics of 'Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays'. Together they form a unique fingerprint.

Cite this