Zusammenfassung
Es werden adaptive Runge-Kutta-Verfahren betrachtet und Stabilitätsuntersuchungen für diese linear impliziten Methoden durchgeführt. Für die Anwendung wird ein LS-stabiles Verfahren vierter Ordnung mit einer angepaßten Schrittweitenkontrolle vorgeschlagen. Testergebnisse von 25 stiff Anfangswertproblemen für verschiedenen Toleranzen werden diskutiert.
Abstract
Adaptive Runge-Kutta-methods are considered. Investigations of stability for these linear implicit methods are studied. For the application a LS-stable method of order four with an adaptive stepsize control is proposed. Test results for 25 stiff initial value problems for different tolerances are discussed.
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Strehmel, K., Weiner, R. Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden. Computing 29, 153–165 (1982). https://doi.org/10.1007/BF02249938
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DOI: https://doi.org/10.1007/BF02249938