Equilibria of Runge-Kutta methods |
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Authors: | E Hairer A Iserles J M Sanz-Serna |
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Institution: | (1) Section de Mathématiques, Université de Genève, Switzerland;(2) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK;(3) Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, Spain |
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Abstract: | Summary 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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Keywords: | AMS(MOS): 65L05 CR: G1 7 |
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