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Numerical Algorithms

, Volume 78, Issue 4, pp 1001–1017 | Cite as

Shrink wrapping for Taylor models revisited

  • Florian BüngerEmail author
Original Paper
  • 43 Downloads

Abstract

Taylor models have been used successfully to calculate verified inclusions of the solutions of initial value problems for ordinary differential equations. In this context, Makino and Berz introduced an accompanying method called shrink wrapping. This method aims to reduce the wrapping effect which occurs during repeated forward integration of Taylor models. We review shrink wrapping as proposed by Makino and Berz, state examples that point to a flaw in their theorem and concept of proof, and present a new, corrected version of shrink wrapping.

Keywords

Shrink wrapping Wrapping effect Taylor models Ordinary differential equations 

Mathematics Subject Classifications (2010)

65L05 65L70 65G40 

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Notes

Acknowledgements

I thank Prof. S.M. Rump for many helpful and inspiring discussions of the subject.

References

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Institute for Reliable ComputingHamburg University of TechnologyHamburgGermany

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