New Applications of Taylor Model Methods
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Taylor model methods unify many concepts of high-order computational differentiation with verification approaches covering the Taylor remainder term. 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 optimization, verified quadrature and verified propagation of extended domains of initial conditions through ODEs, approaches towards verified solution of DAEs and PDEs. 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 global optimization, very high-dimensional numeric quadrature, particle accelerators, and dynamics of near-earth asteroids.
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