Shrink wrapping for Taylor models revisited

Publikationstyp
Journal Article
Date Issued
2018-08-01
Sprache
English
Author(s)
Bünger, Florian  
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/2878
Journal
Numerical Algorithms  
Volume
78
Issue
4
Start Page
1001
End Page
1017
Citation
Numerical Algorithms 4 (78): 1001-1017 (2018-08-01)
Publisher DOI
10.1007/s11075-017-0410-1
Scopus ID
2-s2.0-85030157922
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.