A super-attainable order in collocation methods for differential equations with proportional delay

Emiko Ishiwata*, Yoshiaki Muroya, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

We are concerned with the pantograph differential equation y (t) = ay (t) + by (qt) + f (t), t > 0, y (0) = y0, with proportional delay qt, 0 < q < 1. In the literatures, it is known that if we choose some proper m collocation points for m ≥ 2, then collocation leads to a superconvergence result of order p* = 2 m + 1 at the first mesh point t = h. In this paper, in such collocation solution to the above equation, we show that there are cases for some 0 < q < 1 such that the attainable order at the first mesh point t = h, becomes a super-attainable order, just O (h2 m + 2). Numerical experiments of such 0 < q < 1 are also presented.

Original languageEnglish
Pages (from-to)227-236
Number of pages10
JournalApplied Mathematics and Computation
Volume198
Issue number1
DOIs
Publication statusPublished - 15 Apr 2008

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Collocation methods
  • Delay differential equations
  • Proportional delay
  • Super-attainable order

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