Rigorous Reachability Analysis and Domain Decomposition of Taylor Models
AbstractWe 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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