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Accurate numerical approximations to initial value problems with periodical solutions

Genaue numerische Näherungen für Anfangswertprobleme mit periodischen Lösungen

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Abstract

An explicit fourth order Runge-Kutta Fehlberg method for the numerical solution of first order differential equations having oscillating solutions is developed in this paper. This method is constructed using a linear homogeneous test equation with phase-lag of order either six or eight and with dissipative order six. Both the schemes are used for the numerical solution of equations describing free and weakly forced oscillations and semidiscretized hyperbolic equations. The numerical results obtained show that the new method is much more accurate than other methods proposed recently.

Zusammenfassung

In dieser Arbeit wird ein explizites RKF-Verfahren zur numerischen Lösung von Differentialgleichungen 1. Ordnung mit periodischen Lösungen entwickelt. Für eine lineare homogene Testaufgabe ergeben sich dabei eine dissipative Ordnung 6 und Phasenverschiebungen der Ordnung 6 bzw. 8. Beide Varianten werden auf Gleichungen angewandt, die freie oder schwach-erzwungene Schwingungen beschreiben, sowie auf teildiskretisierte hyperbolische Gleichungen. Die numerischen Ergebnisse erweisen das neue Verfahren als wesentlich genauer als andere kürzlich vorgeschlagene Verfahren.

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  1. Informatics Laboratory, Agricultural University of Athens, 75, Iera Odos str, GR-118 55, Athens, Greece

    T. E. Simos & A. B. Sideridis

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  1. T. E. Simos
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  2. A. B. Sideridis
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Simos, T.E., Sideridis, A.B. Accurate numerical approximations to initial value problems with periodical solutions. Computing 50, 87–92 (1993). https://doi.org/10.1007/BF02280042

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  • DOI: https://doi.org/10.1007/BF02280042

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