Abstract
A method is presented for developing Runge-Kutta integration algorithms with built-in estimates of the accumulated truncation error. Several new 2-nd, 3-rd, and 4-th order algorithms are given. The computation per step of the new algorithms is identical to that of algorithms which provide only an estimate of the local truncation error. Numerical experimentation with the new algorithms shows that the estimated error compares very well with the true accumulated error. Further, the error is of the same order as that incurred using traditional Runge-Kutta algorithms.
Zusammenfassung
Es wird eine Methode für die Entwicklung von Runge-Kutta-Integrationsalgorithmen angegeben, die die Schätzung des globalen Verfahrensfehlers ermöglichen. Mehrere neue Algorithmen 2., 3. und 4. Ordnung werden angeführt. Die Rechenarbeit pro Schritt ist identisch für die neuen Algorithmen und für Algorithmen, die nur eine Schätzung des lokalen Verfahrensfehlers ermöglichen. Numerische Versuche mit den neuen Algorithmen ergeben, daß der geschätzte Fehler den wahren akkumulierten Fehler gut wiedergibt. Außerdem ist der Fehler von derselben Ordnung wie bei gewöhnlichen Runge-Kutta-Algorithmen.
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Merluzzi, P., Brosilow, C. Runge-Kutta integration algorithms with built-in estimates of the accumulated truncation error. Computing 20, 1–16 (1978). https://doi.org/10.1007/BF02241897
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DOI: https://doi.org/10.1007/BF02241897