High-order collocation methods for singular Volterra functional equations of neutral type

Hermann BRUNNER*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

In the first part of this paper we present a survey of recent results on the attainable order of (super-) convergence of collocation solutions for systems of Volterra functional integro-differential equations with weakly singular kernels kα and variable delay functions θ (t) = t - τ (t). Related functional equations and theoretical and computational aspects of collocation methods for their solution are also described. The paper concludes with comments on ongoing and possible future work.

Original languageEnglish
Pages (from-to)533-548
Number of pages16
JournalApplied Numerical Mathematics
Volume57
Issue number5-7 SPEC. ISS.
DOIs
Publication statusPublished - May 2007

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Collocation methods
  • Neutral equations
  • Optimal order of convergence
  • Variable delays
  • Volterra functional integro-differential equations
  • Weakly singular kernels

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