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Constructive characterization of A-stable approximations to exp(z) and its connection with algebraically stable Runge-Kutta methods

ContributorsHairer, Ernst
Published inNumerische Mathematik, vol. 39, no. 2, p. 247-258
Publication date1982
Abstract

All rational approximations to exp(z) of order >=2m-beta (m denotes the maximal degree of nominator and denominator) are given by a closed formula involving beta real parameters. Using the theory of order stars [9], necessary and sufficient conditions for A-stability (respectively I-stability) are given. On the basis of this characterization relations between the concepts of A-stability and algebraic stability (for implicit Runge-Kutta methods) are investigated. In particular we can partly prove the conjecture that to any irreducible A-stable R(z) of oder >=0 there exist algebraically stable Runge-Kutta methods of the same order with R(z) as stability function.

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Citation (ISO format)
HAIRER, Ernst. Constructive characterization of A-stable approximations to exp(z) and its connection with algebraically stable Runge-Kutta methods. In: Numerische Mathematik, 1982, vol. 39, n° 2, p. 247–258. doi: 10.1007/BF01408698
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