Numerische Mathematik

, Volume 41, Issue 3, pp 399–422 | Cite as

Order and stepsize control in extrapolation methods

  • P. Deuflhard


The paper presents a new theory for joint order and stepsize control in extrapolation methods. This theory defines a locally optimal order that can be determined along any trajectory to be computed. In addition, Shannon's information theory is applied to derive some ideal convergence model that is expected to describe the behavior of an extrapolation method over a large set of test problems. Extensive numerical comparisons document a drastic acceleration in stiff integration and a mild acceleration in non-stiff integration by the new device. Moreover, a significant increase in reliability, robustness, and portability of the extrapolation codes is achieved.

Subject Classifications

AMS(MOS): 65L05 CR: 5.17 


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • P. Deuflhard
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelberg 1 (Fed. Rep.)

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