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A(α)-stable cyclic composite multistep methods of order 5

A(α)-stabile zykische Verfahren der Ordnung 5

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Abstract

We describe a newA(α)-stable 3-cyclic 3-step method with accuracy of orderP=5. This is in contrast to the originally developed methods [5] which have greater order of accuracy (P=6) but a small stability region. Moreover, the new method shows slightly better stability than the backward differentiation formula (BDF) [6] of the same order.

Zusammenfassung

Es wird ein neuesA(α)-stabiles 3-zyklisches 3-Schritt-Verfahren der OrdnungP=5 entwickelt, im Gegensatz zu den in [5] ursprünglich entwickelten Verfahren, die sich durch höhere Ordnung (P=6) auszeichnen, aber kleine Stabilitätsbereiche haben. Das neue Verfahren besitzt außerdem etwas bessere Stabilitätseigenschaften als das in [6] (Gear) gegebene Verfahren mit der gleichen Ordnung.

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Authors and Affiliations

  1. Kernforschungsanlage Jülich, Institut für Festkörperforschung, Postfach 1913, D-5170, Jülich, Federal Republic of Germany

    M. Mihelčić

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  1. M. Mihelčić
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Mihelčić, M. A(α)-stable cyclic composite multistep methods of order 5. Computing 20, 267–272 (1978). https://doi.org/10.1007/BF02251950

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