Higher order verified inclusions of multidimensional systems by Taylor models

Different from floating point computations, interval methods provide rigoro us enclosures of functions, however the limitation of the methods is the ov erestimation mostly caused by the lack of information on functional depende ncy. The first cure to the problem is to use a smaller domain, but when a f unction is complicated, as it often is for practical problems, the number o f subdivisions becomes quite large. In case of multidimensional systems, th e computational expense by simple interval methods increases astronomically . A new approach, the Taylor model method, models a function by a higher or der polynomial which keeps the majority of the functional dependency, and a n interval which contains the small remaining error. The method naturally s uppresses the dependency problem, and proves particularly effective for the treatment of complicated multidimensional systems.