Abstract
We shall give a constructive characterization of all irreducible B -stable Runge-Kutta methods (Theorem 13.15). Because of Theorem 12.16 we first have to study quadrature formulas with positive weights.
Bien que le problème (des quadratures) ait une durée de deux cents ans à peu près, bien qu’il était l’objet de nombreuses recherches de plusieurs géomètres: Newton, Cotes, Gauss, Jacobi, Hermite, Tchébychef, Christoffel, Heine, Radeau [sic], A. Markov, T. Stitjes [sic], C. Possé, C. Andréev, N. Sonin et d’autres, il ne peut être considéré, cependant, comme suffisamment épuisé.
(V. Steklov 1917)
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© 1996 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G. (1996). Positive Quadrature Formulas and B-Stable RK-Methods. In: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05221-7_13
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DOI: https://doi.org/10.1007/978-3-642-05221-7_13
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