A necessary condition forB-convergence of Runge-Kutta methods |
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Authors: | J Schneid |
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Institution: | (1) Institut für Angewandte und Numerische Mathematik, Technical University of Vienna, Wiedner Hauptstrasse 8–10, A-1040 Vienna, Austria |
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Abstract: | Algebraic stability is a well-known property necessary forB-convergence of a Runge-Kutta method, provided its nodesc
i
are such thatc
i
– c
j
wheneveri j. In this paper a slightly weaker property is established which becomes algebraic stability as soon asc
i
– c
j
, wheneveri j is excluded.Using this condition it is shown that the Lobatto IIIA methods with more than two stages cannot beB-convergent.This paper was written while the author was visiting the Rijksuniversiteit Leiden in the Netherlands, supported by the Netherlands Organization for Scientific Research (N.W.O.) and by an Erwin Schrödinger scholarship from the Fonds zur Förderung der wissenschaftlichen Forschung. |
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Keywords: | AMS 65L05 |
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