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On the relation between stability and contractivity

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Abstract

This paper concerns the rate of growth of numerical approximations obtained by one-step methods for solving linear stiff initial value problems. For some of these methods weak stability with respect to arbitrary norms is shown to be equivalent to contractivity. This kind of stability is also proved to entail a barrierp≦1 for the order of accuracyp within a broad class of methods, including general Runge-Kutta methods withm≧1 stages.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Computer Science, University of Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

    M. N. Spijker

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  1. M. N. Spijker
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Dedicated to Professor Germund Dahlquist on the occasion of his sixtieth birthday.

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Spijker, M.N. On the relation between stability and contractivity. BIT 24, 656–666 (1984). https://doi.org/10.1007/BF01934922

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  • DOI: https://doi.org/10.1007/BF01934922

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