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A stability property of implicit Runge-Kutta methods

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Abstract

A class of implicit Runge-Kutta methods is shown to possess a stability property which is a natural extension of the notion ofA-stability for non-linear systems.

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References

  1. G. Dahlquist,Error Analysis for a Class of Methods for Stiff Non-linear Initial Value Problems, to be published in the Proceedings of the Conference on Numerical Analysis, Dundee, 1975.

  2. J. C. Butcher,Implicit Runge-Kutta Processes, Math. Comp. 18 (1964), 50–64.

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  3. B. L. Ehle,On Padé Approximation to the Exponential Function and A-stable Methods for the Numerical Solution of Initial Value Problems Research Report CSRR 2010, Dept. AACS, University of Waterloo.

  4. F. H. Chipman,A-stable Runge-Kutta Processes, BIT 11 (1971), 384–388.

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Butcher, J.C. A stability property of implicit Runge-Kutta methods. BIT 15, 358–361 (1975). https://doi.org/10.1007/BF01931672

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  • DOI: https://doi.org/10.1007/BF01931672

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