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Rigorous Reachability Analysis and Domain Decomposition of Taylor Models

Abstract

We present mathematically rigorous computational methods for the transport of large domains through ODEs with the goal of making rigorous statements about their long term evolution. Of particular interest are determination of locations of attractors, reachability of certain sets, and proof of non-reachability of others. The methods are based on Taylor model verified integrators for the propagation of large domains, and heavily rely on automatic domain decomposition for accuracy. We illustrate the behavior and performance of these methods using several commonly studied dynamical systems.

M. Berz, K. Makino, Lecture Notes in Computer Science 10381 (2017) 90-97

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