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Rigorous error bounds for RK methods in the proof of chaotic behaviour

✍ Scribed by Arno Berger

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
202 KB
Volume
111
Category
Article
ISSN
0377-0427

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✦ Synopsis

Complicated dynamical systems can be rigorously analysed by means of Conley index theory. Due to its partly numerical nature such an analysis necessitates bounds on the truncation and the round-o error. These are provided for explicit RK methods in the form of iteration schemes ready-made for applications. The presentation is aimed to simplify error bounds already available so that di erent error sources can be clearly overlooked. As an immediate application, a computer-assisted analysis elucidates the intricate dynamics of a simple mechanical system.

πŸ“œ SIMILAR VOLUMES

Comparison of methods for solving sets o
Comparison of methods for solving sets of linear inequalities in the bounded-error context
✍ HΓ©lΓ¨ne Piet-Lahanier; SΓ‘ndor M. Veres; Eric Walter πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 818 KB

Piet-Lahanier, H., S.M. Veres and E. Walter, Comparison of methods for solving sets of linear inequalities in the bounded-error context, Mathematics and Computers in Simulation 34 (1992) 515-524. Effective recursive updating of the solution set of linear inequalities has recently gained importance i