New Applications of Taylor Model Method
by
Kyoko Makino
Coauthors: Martin Berz

Taylor model methods represent a unification of many concepts of high-order computational differentiation with verification approaches. Not only do they provide local multivariate derivatives, they also allow for highly efficient and sharp verification. We present several recent results obtained with Taylor model methods, including verified propagation of extended domains of initial conditions through ODEs, approaches towards verified solution of DAEs and PDEs, verified optimization, and verified quadrature. In all cases, the methods allow the development of new numeric-analytic tools that efficiently capitalize on the availability of derivatives and sharp inclusions over extended ranges. Applications of the methods are given, including dynamics of near-earth asteroids, particle accelerators, global optimization, and very high-dimensional numeric quadrature.

http://bt.nscl.msu.edu/~hoefkens/ad2000-rda.ps

Date received: March 3, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-95.