Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type

Hermann Brunner*, Qiumei Huang, Hehu Xie

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

65 Citations (Scopus)
5 Downloads (Pure)

Abstract

This paper is concerned with the application of the discontinuous Galerkin method to delay differential equations with vanishing delay qt (0 < q < 1). Our aim is to establish optimal global and local superconvergence results on uniform meshes and compare these with analogous estimates for collocation methods. The theoretical results are illustrated by a broad range of numerical examples.

Original languageEnglish
Pages (from-to)1944-1967
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number5
DOIs
Publication statusPublished - 30 Nov 2010

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Discontinuous Galerkin method
  • Optimal order of superconvergence
  • Pantograph delay differential equations
  • Vanishing proportional delay

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