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Equilibria of Runge-Kutta methods

Iserles, Arieh
Sanz-Serna, Jesus Maria
Published in Numerische Mathematik. 1990, vol. 58, no. 1, p. 243-254
Abstract It is known that certain Runge-Kutta methods share the property that, in a constant-step implementation, if a solution trajectory converges to a bounded limit then it must be a fixed point of the underlying differential system. Such methods are calledregular. In the present paper we provide a recursive test to check whether given method is regular. Moreover, by examining solution trajectories of linear equations, we prove that the order of ans-stage regular method may not exceed 2[(s+2)/2] and that the maximal order of regular Runge-Kutta method with an irreducible stability function is 4.
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HAIRER, Ernst, ISERLES, Arieh, SANZ-SERNA, Jesus Maria. Equilibria of Runge-Kutta methods. In: Numerische Mathematik, 1990, vol. 58, n° 1, p. 243-254. doi: 10.1007/BF01385623 https://archive-ouverte.unige.ch/unige:12475

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Deposited on : 2010-11-16

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