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Experiments with a variable-order type 1 DIMSIM code

Numerical Algorithms volume 22, pages 237–261 (1999)Cite this article

Abstract

The issues related to the development of a new code for nonstiff ordinary differential equations are discussed. This code is based on the Nordsieck representation of type 1 DIMSIMs, implemented in a variable-step size variable-order mode. Numerical results demonstrate that the error estimation employed in the code is very reliable and that the step and order changing strategies are very robust. This code outperforms the Matlab ode45 code for moderate and stringent tolerances.

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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. Experiments with a variable-order type 1 DIMSIM code. Numerical Algorithms 22, 237–261 (1999). https://doi.org/10.1023/A:1019135630307

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  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019135630307

  • DIMSIM methods
  • Nordsieck representation
  • local error estimation
  • step size and order changing strategy
  • 65L05