Abstract
Interpolants locally of the fifth and sixth orders are constructed by means of the boot-strapping method of Enright et al. for the Runge-Kutta pairs (globally) of the fourth and fifth orders of Dormand and Prince DP(4,5)6M, 7M, 7C and 7S. The asymptotic errors in the interpolants are found to be bounded, in the uniform norm in the space of elementary differentials, by the error in the discrete solution. Numerical results corroborate these asymptotic bounds at working step sizes.
Zusammenfassung
Interpolierende von lokal fünfter und sechster Ordnung werden mit Enright's “boot-strapping” Methode für Runge-Kutta Paare vierter und fünfter Ordnung von Dormand und Prince DP(4,5)6M, 7M, 7C und 7S konstruiert. Bezüglich der gleichmäßigen Norm in Raum der elementaren Differentiale erweist sich der asymptotische Fehler der Interpolierenden als beschränkt duch den Fehler der diskreten Lösung. Numerische Ergebnisse bestätigen diese asymptotischen Schranken bei der gewählten Schrittweite.
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References
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This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under grant A 7691.
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Calvé, M., Vaillancourt, R. Interpolants for Runge-Kutta pairs of order four and five. Computing 45, 383–388 (1990). https://doi.org/10.1007/BF02238806
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DOI: https://doi.org/10.1007/BF02238806