Superconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays

A. Bellen*, Hermann BRUNNER, S. Maset, L. Torelli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We study the optimal orders of (global and local) superconvergence in piecewise polynomial collocation on quasi-graded meshes for functional differential equations with (nonlinear) delays vanishing at t=0. It is shown that while for linear delays (e.g. proportional delays qt with 0<q<1) and certain nonlinear delays the classical optimal order results still hold, high degree of tangency with the identity function at t=0 leads not only to a reduction in the order of superconvergence but also to very serious difficulties in the actual computation of numerical approximations.

Original languageEnglish
Pages (from-to)229-247
Number of pages19
JournalBIT Numerical Mathematics
Volume46
Issue number2
DOIs
Publication statusPublished - Jun 2006

Scopus Subject Areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Collocation methods
  • Functional differential equations
  • Optimal order of superconvergence
  • Order reduction
  • Quasi-graded meshes
  • Vanishing delays
  • Volterra integro-differential equations

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