Local error estimation for singly-implicit formulas by two-step Runge- Kutta methods (Q688737)
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scientific article; zbMATH DE number 438471
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local error estimation for singly-implicit formulas by two-step Runge- Kutta methods |
scientific article; zbMATH DE number 438471 |
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Local error estimation for singly-implicit formulas by two-step Runge- Kutta methods (English)
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5 April 1994
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The authors show that the local discretization error of \(s\)-stage singly- implicity Runge-Kutta methods of order \(p\) can be estimated by embedding these methods into \(s\)-stage two-step Runge-Kutta methods of order \(p+1\), where \(p=s\) or \(p=s+1\). The new estimations do not need any extra evaluations of the right hand side of the differential equation. Concrete formulae and numerical examples are also given.
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local discretization error
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\(s\)-stage singly-implicity Runge-Kutta methods
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\(s\)-stage two-step Runge-Kutta methods
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numerical examples
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0.91530395
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0.90654904
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0.89812714
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0.8938124
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0.8855685
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