Rigorous error bounds for RK methods in the proof of chaotic behaviour (Q1964098)
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scientific article; zbMATH DE number 1398815
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rigorous error bounds for RK methods in the proof of chaotic behaviour |
scientific article; zbMATH DE number 1398815 |
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Rigorous error bounds for RK methods in the proof of chaotic behaviour (English)
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20 July 2000
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The paper presents rigorous bounds on the truncation, the round-off and the global error for the numerical integration of ordinary differential equations by means of explicit Runge-Kutta methods. These are provided in the form of iteration schemes ready-made for applications. The Conley index is used to develop an elegant tool for analyzing dynamical systems by means of computers. In order to demonstrate how the findings fit into the framework of the Conley index theory, the dynamics of a pendulum with oscillating support is investigated using a computer-assisted analysis.
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explicit Runge-Kutta methods
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truncation error
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round-off error
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chaotic behaviour
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iteration schemes
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Conley index
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dynamical systems
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pendulum
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0.7436201572418213
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0.7324786186218262
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