Abstract
In this note the exact order ofB-convergence is determined for them-stage Gaussian Runge-Kutta method. Form=1 this order is 2, whereas form≥2 this order turns out to be onlym.
Zusammenfassung
In dieser Note bestimmen wir die exakteB-Konvergenzordnung desm-stufigen Gauss'schen Runge-Kutta Verfahrens. Fürm=1 ist diese Ordnung 2, während sich fürm≥2 nurm als Ordnung ergibt.
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References
Ascher, V., Bader, G.: Stability of collocation at Gaussian points. Tech. Rep. 84-13, Departm. Comp. Sc. Univ. British Columbia, Vancouver (1984).
Burrage, K., Butcher, J. C.: Stability criteria for implicit Runge-Kutta methods. SIAM J. Numer. Anal.16, 46–57 (1979).
Burrage, K., Hundsdorfer, W. H., Verwer, J. G.: A study ofB-convergence of Runge-Kutta methods. Computing (this issue).
Crouzeix, M.: Sur laB-stabilité des méthodes de Runge-Kutta. Numer. Math.32, 75–82 (1979).
Crouzeix, M., Raviart, P. D.: Méthodes de Runge-Kutta. Lecture notes, Université de Rennes (1980).
Dekker, K., Verwer, J. G.: Stability of Runge-Kutta methods for stiff nonlinear differential equations. Amsterdam, New York, Oxford: North Holland Publ. Comp. (1984).
Frank, R., Schneid, J., Ueberhuber, C. W.: Order results for implicit Runge-Kutta methods applied to stiff systems. SIAM J. Numer. Anal.22, 515–534 (1985).
Kraaijevanger, J. F. B. M.:B-convergence of the implicit midpoint rule and the trapezoidal rule. Rep. 01-85, Inst. Appl. Math. Comp. Sc. Univ. Leiden (1985). To appear in BIT.
Montijano, J. I.: Estudio de los metodos SIRK para la resolucion numérica de ecuaciones diferenciales de tipo stiff. Thesis, University of Zaragoza (1983).
Stetter, H. J.: ZurB-Konvergenz der impliziten Trapez- und Mittelpunktregel. Unpublished note (1982).
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Dekker, K., Kraaijevanger, J.F.B.M. & Spijker, M.N. The order of B-convergence of the Gaussian Runge-Kutta method. Computing 36, 35–41 (1986). https://doi.org/10.1007/BF02238190
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DOI: https://doi.org/10.1007/BF02238190