Towards a computer-assisted proof for chaos in a forced damped pendulum equation

Tibor Csendes, Balázs Bánhelyi, László Hatvani

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We report on the first steps made towards the computational proof of the chaotic behaviour of the forced damped pendulum. Although, chaos for this pendulum was being conjectured for long, and it has been plausible on the basis of numerical simulations, there is no rigorous proof for it. In the present paper we provide computational details on a fitting model and on a verified method of solution. We also give guaranteed reliability solutions showing some trajectory properties necessary for complicate chaotic behaviour.

Original languageEnglish
Pages (from-to)378-383
Number of pages6
JournalJournal of Computational and Applied Mathematics
Volume199
Issue number2
DOIs
Publication statusPublished - Feb 15 2007

Keywords

  • Chaos
  • Differential equations
  • Interval method
  • Pendulum

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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