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OnA-stable implicit Runge-Kutta methods

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Abstract

An elementary proof is given of theA-stability of implicit Runge-Kutta methods for which the corresponding rational function is on the diagonal or one of the first two subdiagonals of the Padé table for the exponential function. The result is extended to give necessary and sufficient conditions for theA-stability ofn-stage methods of order greater than or equal to 2n−2.

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References

  1. G. A. Baker,Essentials of Padé approximants, Academic Press, 1975.

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Authors and Affiliations

  1. Department of Mathematics, The University of Auckland, Auckland, New Zealand

    J. C. Butcher

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  1. J. C. Butcher
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Butcher, J.C. OnA-stable implicit Runge-Kutta methods. BIT 17, 375–378 (1977). https://doi.org/10.1007/BF01933446

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  • DOI: https://doi.org/10.1007/BF01933446

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