Rigorous computational shadowingof orbits of ordinary differential equations

Brian A Coomes, H\"useyin Ko\c cak, Kenneth J. Palmer

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

The existence of a true orbit near a numericallycomputed approximate orbit -- shadowing -- ofautonomous system of ordinary differential equationsis investigated.A general shadowing theorem for finite time,which guarantees the existence of shadowingin ordinary differential equationsand provides error bounds for the distance betweenthe true and the approximate orbit in terms of computablequantities, is proved.The practical use and the effectiveness of this theoremis demonstrated in the numerical computationsof chaotic orbits of the Lorenz equations.

Original languageEnglish (US)
Pages (from-to)401-421
Number of pages21
JournalNumerische Mathematik
Volume69
Issue number4
DOIs
StatePublished - 1995

Fingerprint

Ordinary differential equations
Ordinary differential equation
Orbits
Orbit
Shadowing
Lorenz Equations
Error Bounds
Theorem

Keywords

  • Mathematics Subject Classification (1991): 65L05

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Rigorous computational shadowingof orbits of ordinary differential equations. / Coomes, Brian A; Ko\c cak, H\"useyin; Palmer, Kenneth J.

In: Numerische Mathematik, Vol. 69, No. 4, 1995, p. 401-421.

Research output: Contribution to journalArticle

Coomes, Brian A ; Ko\c cak, H\"useyin ; Palmer, Kenneth J. / Rigorous computational shadowingof orbits of ordinary differential equations. In: Numerische Mathematik. 1995 ; Vol. 69, No. 4. pp. 401-421.
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