On the stability of numerical methods of Hopf points using backward error analysis (Q1895656)
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scientific article; zbMATH DE number 783953
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the stability of numerical methods of Hopf points using backward error analysis |
scientific article; zbMATH DE number 783953 |
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On the stability of numerical methods of Hopf points using backward error analysis (English)
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11 March 1996
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The author uses backward error analysis to analyse the behavior of several Runge-Kutta and Adams formulas on two basic classes of problems. One has the equation as a normal form on a center manifold. The other is for problems with weakly attracting periodic solutions. For many methods, a Hopf bifurcation for maps occurs. For a special case, the effect of an adaptive mesh selection procedure on the results is presented.
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Poincaré map
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Runge-Kutta method
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Adams method
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stability
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backward error analysis
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weakly attracting periodic solutions
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Hopf bifurcation
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adaptive mesh selection
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