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Zbl 1055.65095
Makino, Kyoko; Berz, Martin
Taylor models and other validated functional inclusion methods. (English)
[J] Int. J. Pure Appl. Math. 6, No. 3, 239-316 (2003). ISSN 1311-8080

The authors give a review of Taylor model methods for validated computation and compares the efficacy of a number of different approaches. Arithmetics for effective computation of Taylor model methods are presented along with a number of algorithms for computing a variety of analytic operations.
[Kevin Burrage (Brisbane)]

MSC 2000:: *65L20 Stability of numerical methods for ODE
65L06 Multistep, Runge-Kutta, and extrapolation methods
65G20 Algorithms with automatic result verification
34A60 ODE with multivalued right-hand sides

Keywords: Taylor model methods; validated computation; algorithms

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Zentralblatt MATH Berlin [Germany]