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Changing stepsize in the integration of differential equations using modified divided differences

Part of the Lecture Notes in Mathematics book series (LNM,volume 362)

Abstract

Multistep methods for solving differential equations based on numerical integration formulas or numerical differentiation formulas (for stiff equations) require special provision for changing the stepsize. New algorithms are given which make the use of modified divided differences an attractive way to carry out the change in stepsize for such methods. Error estimation and some of the important factors in stepsize selection and the selection of integration order are also considered.

Keywords

  • Local Error
  • Variable Order
  • Multistep Method
  • Divided Difference
  • Differentiation Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS7-100, sponsored by the National Aeronautics and Space Administration.

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© 1974 Springer-Verlag

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Krogh, F.T. (1974). Changing stepsize in the integration of differential equations using modified divided differences. In: Bettis, D.G. (eds) Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations. Lecture Notes in Mathematics, vol 362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066584

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  • DOI: https://doi.org/10.1007/BFb0066584

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06602-6

  • Online ISBN: 978-3-540-37911-9

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