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A new approach to error estimation for general linear methods

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Summary.

We present a simple, accurate and reliable approach to the estimation of the local discretization error for general linear methods for ordinary differential equations. In this approach the input vector for the next step from x n to x n+1 =x n +h is rescaled and modified accordingly to compensate for the change of stepsize from ¯h to h=r¯h.

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References

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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. Department of Mathematics, Arizona State University, Tempe, Arizona, 85287

    Z. Jackiewicz

Authors
  1. J.C. Butcher
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  2. Z. Jackiewicz
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Corresponding author

Correspondence to Z. Jackiewicz.

Additional information

The work of the first author was assisted by the Marsden Fund of New Zealand

The work of the second author was partially supported by the National Science Foundation under grant NSF DMS–9971164 and by the Auckland Mathematics & Computation Ltd.

Mathematics Subject Classification (2000): 65L05

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Butcher, J., Jackiewicz, Z. A new approach to error estimation for general linear methods. Numer. Math. 95, 487–502 (2003). https://doi.org/10.1007/s00211-002-0452-7

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  • DOI: https://doi.org/10.1007/s00211-002-0452-7

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