Stability of Runge-Kutta methods used in modular integration
نویسندگان
چکیده
منابع مشابه
Stability of Runge-kutta Methods Used in Modular Integration
A pair of Runge-Kutta methods is applied to a system of ordinary diierential equations in a modular fashion known as time point relaxation. For a class of two by two linear systems with constant coeecients, the concept of coupling stability is introduced. This is way of measuring the loss of stability due to the decoupling of the system into two scalar subsystems. The strategy for handling the ...
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In this paper, a general and detailed study of linear stability of Runge–Kutta–Nyström (RKN) methods is given. In the case that arbitrarily stiff problems are integrated, we establish a condition that RKN methods must satisfy so that a uniform bound for stability can be achieved. This condition is not satisfied by any method in the literature. Therefore, a stable method is constructed and some ...
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Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1995
ISSN: 0377-0427
DOI: 10.1016/0377-0427(94)00078-6