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Largest disk of stability of explicit Runge-Kutta methods

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Abstract

The stability region of an explicit and consistentm-stage Runge-Kutta method cannot contain the closed disk with diameter [−2m, 0] as a proper subset.

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References

  1. G. Dahlquist,Positive functions and some applications to stability questions for numerical methods, in “Recent Advances in Numerical Analysis”, ed. C. de Boor and G. Golub, Acad. Press (1978).

  2. R. Jeltsch and O. Nevanlinna,Stability of explicit time discretization. To appear as Report of the Department of Mathematics, Oulu University.

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Authors and Affiliations

  1. Institute of Mathematics, Ruhr-University Bochum, D-4630, Bochum, Germany

    Rolf Jeltsch & Olavi Nevanlinna

  2. Mathematics Department, Oulu University, Oulu, Finland

    Rolf Jeltsch & Olavi Nevanlinna

Authors
  1. Rolf Jeltsch
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  2. Olavi Nevanlinna
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Jeltsch, R., Nevanlinna, O. Largest disk of stability of explicit Runge-Kutta methods. BIT 18, 500–502 (1978). https://doi.org/10.1007/BF01932030

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  • DOI: https://doi.org/10.1007/BF01932030

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