An algebraic characterization ofB-convergent Runge-Kutta methods |
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Authors: | Willem H Hundsdorfer Josef Schneid |
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Institution: | (1) Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands;(2) Institut für Angewandte und Numerische Mathematik, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria |
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Abstract: | Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung |
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Keywords: | AMS(MOS): 65L05 CR: G1 7 |
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