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Dahlquist's first barrier for multistage multistep formulas

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Abstract

Dahlquist's proof of his barrier for the order of stable linear multistep methods is combined with Reimer's proof of the corresponding barrier for multistep multiderivative methods. This leads to a shortening of Reimer's original proof and gives lower bounds for the error constant. These bounds are then studied for high error order and are used to model the optimal order and stepsize selection in an idealized integration code.

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References

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Authors and Affiliations

  1. Institut für Geometrie and Praktische Mathematik, RWTH Aachen, D-5100, Aachen, Fed. Rep. Germany

    Rolf Jeltsch & Olavi Nevanlinna

  2. Institute of Mathematics, Helsinki University of Technology, SF-02150, Espoo 15, Finland

    Rolf Jeltsch & Olavi Nevanlinna

Authors
  1. Rolf Jeltsch
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  2. Olavi Nevanlinna
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Additional information

Dedicated to Professor Germund Dahlquist on the occasion of his sixtieth birthday.

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Jeltsch, R., Nevanlinna, O. Dahlquist's first barrier for multistage multistep formulas. BIT 24, 538–555 (1984). https://doi.org/10.1007/BF01934912

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  • DOI: https://doi.org/10.1007/BF01934912

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