Constructive characterization ofA-stable approximations to exp(z) and its connection with algebraically stable Runge-Kutta methods |
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Authors: | E Hairer |
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Institution: | (1) Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293, 6900 Heidelberg 1, FRG |
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Abstract: | Summary All rational approximations to exp(z) of order 2m– (m denotes the maximal degree of nominator and denominator) are given by a closed formula involving real parameters. Using the theory of order stars 9], necessary and sufficient conditions forA-stability (respectivelyI-stability) are given. On the basis of this characterization relations between the concepts ofA-stability and algebraic stability (for implicit Runge-Kutta methods) are investigated. In particular we can partly prove the conjecture that to any irreducibleA-stableR(z) of oderp 0 there exist algebraically stable Runge-Kutta methods of the same order withR(z) as stability function. |
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Keywords: | AMS(MOS) 65L05 CR 5 17 |
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