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A- and B-stability for Runge-Kutta methods-characterizations and equivalence

Published in Numerische Mathematik. 1986, vol. 48, no. 4, p. 383-389
Abstract Using a special representation of Runge-Kutta methods (W-transformation), simple characterizations of A-stability and B-stability have been obtained in [9, 8, 7]. In this article we will make this representation and their conclusions more transparent by considering the "exact Runge-Kutta method". Finally we demonstrate by a numerical example that for difficult problems B-stable methods are superior to methods which are only A-stable.
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HAIRER, Ernst. A- and B-stability for Runge-Kutta methods-characterizations and equivalence. In: Numerische Mathematik, 1986, vol. 48, n° 4, p. 383-389. doi: 10.1007/BF01389646 https://archive-ouverte.unige.ch/unige:12468

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Deposited on : 2010-11-15

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