Shadowing orbits of ordinary differential equations

Brian A. Coomes, Hüseyin Koçak, Kenneth J. Palmer

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

A new notion of shadowing of a pseudo orbit, an approximate solution, of an autonomous system of ordinary differential equations by an associated nearby true orbit is introduced. Then a general shadowing theorem for finite time, which guarantees the existence of shadowing in ordinary differential equations and provides error bounds for the distance between the true and the pseudo orbit in terms of computable quantities, is proved. The use of this theorem in numerical computations of orbits is outlined.

Original languageEnglish (US)
Pages (from-to)35-43
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume52
Issue number1-3
DOIs
StatePublished - Jul 20 1994

Keywords

  • Chaos
  • Numerical orbits
  • Ordinary differential equations
  • Shadowing

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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