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Nordsieck representation of DIMSIMs

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Abstract

A new representation for diagonally implicit multistage integration methods (DIMSIMs) is derived in which the vector of external stages directly approximates the Nordsieck vector. The methods in this formulation are zero-stable for any choice of variable mesh. They are also easy to implement since changing step-size corresponds to a simple rescaling of the vector of external approximations. The paper contains an analysis of local truncation error and of error accumulation in a variable step-size situation.

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Authors and Affiliations

  1. Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand

    J.C. Butcher

  2. INRIA, Campus Universitaire de Beaulieu, F-35042, Rennes Cedex, France

    P. Chartier

  3. Department of Mathematics, Arizona State University, Tempe, AZ, 85287, USA

    Z. Jackiewicz

Authors
  1. J.C. Butcher
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  2. P. Chartier
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  3. Z. Jackiewicz
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Butcher, J., Chartier, P. & Jackiewicz, Z. Nordsieck representation of DIMSIMs. Numerical Algorithms 16, 209–230 (1997). https://doi.org/10.1023/A:1019195215402

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  • DOI: https://doi.org/10.1023/A:1019195215402

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