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Taylor models and other validated functional inclusion methods. (English) Zbl 1055.65095

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.

MSC:

65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65G20 Algorithms with automatic result verification
34A60 Ordinary differential inclusions

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