Stability of collocation methods for delay differential equations with vanishing delays

Hermann BRUNNER*, Hui Liang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0<q<1) (pantograph DDEs). It is shown that if the collocation points are such that the analogous collocation solution for ODEs is A-stable, then this asymptotic behaviour is inherited by the collocation solution for the pantograph DDE.

Original languageEnglish
Pages (from-to)693-711
Number of pages19
JournalBIT Numerical Mathematics
Volume50
Issue number4
DOIs
Publication statusPublished - Dec 2010

Scopus Subject Areas

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

User-Defined Keywords

  • Asymptotic stability on uniform meshes
  • Collocation methods
  • Delay differential equations
  • Implicit Runge-Kutta methods
  • Pantograph equation
  • Proportional vanishing delay

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