A spectral method for pantograph-type delay differential equations and its convergence analysis

Ishtiaq Ali*, Hermann BRUNNER, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Citations (Scopus)

Abstract

We propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially provided that the data in the given pantograph delay differential equation are smooth.

Original languageEnglish
Pages (from-to)254-265
Number of pages12
JournalJournal of Computational Mathematics
Volume27
Issue number2
Publication statusPublished - Mar 2009

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Spectral methods; Legendre quadrature formula; Pantograph-type delay differential equations; Error analysis; Exponential convergence

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