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A study of B-convergence of Runge-Kutta methods

Eine Untersuchung über B-Konvergenz von Runge-Kutta Verfahren

Abstract

This paper deals with the convergence analysis of implicit Runge-Kutta methods as applied to stiff, semilinear systems of the form\(\dot U\) (t)=QU(t)+g(t, U(t)). A criterion is developed which determines whether the order of optimalB-convergence is at least equal to the stage order or one order higher. This criterion is studied for a number of interesting classes of methods.

Zusammenfassung

Dieser Aufsatz befaßt sich mit der Analyse der Konvergenz von impliziten Runge-Kutta Verfahren für steife, semi-lineare Systeme der Form\(\dot U\) (t)=QU(t)+g(t, U(t)). Ein Kriterium wird entwickelt, welches entscheidet, ob die Ordnung der optimalenB-Konvergenz mindestens gleich der Stufenordnung oder um eine Ordnung höher ist. Dieses Kriterium wird untersucht für eine Zahl von interessanten Klassen von Verfahren.

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Burrage, K., Hundsdorfer, W.H. & Verwer, J.G. A study of B-convergence of Runge-Kutta methods. Computing 36, 17–34 (1986). https://doi.org/10.1007/BF02238189

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AMS Subject Classification

  • 65L05

C R number

  • 5.17

Key words

  • Numerical analysis
  • implicit Runge-Kutta methods
  • stiff problems
  • B-convergence