From Taylor Series to Taylor Models
AbstractAn overview of the background of Taylor series methods and the
utilization of the differential algebraic structure is given, and various
associated techniques are reviewed. The conventional Taylor methods are
extended to allow for a rigorous treatment of bounds for the remainder of
the expansion in a similarly universal way. Utilizing differential algebraic
and functional analytic arguments on the set of Taylor models, arbitrary
order integrators with rigorous remainder treatment are developed. The
integrators can meet pre-specified accuracy requirements in a mathematically
strict way, and are a stepping stone towards fully rigorous estimates of
stability of repetitive systems.
M. Berz, Chapter in: "Nonlinear Problems in Accelerator Physics" (1997) 1-27,
American Institute of Physics CP405
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