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Some old and new Runge-Kutta formulas with stepsize control and their error coefficients

Einige alte und neue Runge-Kutta-Formeln mit Schrittweiten Kontrolle und ihre Fehler-Koeffizienten

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Abstract

The author derives a variant of his earlier 5(6)-th and 7(8)-th order Runge-Kutta formulas. The new formulas are also applicable to quadrature problems. Their error coefficients are of about the same magnitude as those of the earlier formulas, but considerably smaller than those of corresponding formulas of J. H. Vermen.

Zusammenfassung

Der Autor leitet eine Variante seiner früheren Runge-Kutta-Formeln 5(6)-ten und 7(8)-ter Ordnung her. Die neuen Formeln sind auch auf Quadratun-Probleme anwendbar. Ihre Fehler-Koeffizienten sind von ungefähr der gleichen Größe wie die der früheren Formeln, aber erheblich kleiner als die entsprechender Formeln von J. H. Vernen.

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References

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  1. Marshall Space Flight Center, Huntsville, NASA, 2113 Fairfax Street NE, 35811, Huntsville, AL, USA

    E. Fehlberg

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  1. E. Fehlberg
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Fehlberg, E. Some old and new Runge-Kutta formulas with stepsize control and their error coefficients. Computing 34, 265–270 (1985). https://doi.org/10.1007/BF02253322

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  • DOI: https://doi.org/10.1007/BF02253322

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