SUNDIALS

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چکیده

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Sundials and Mathematical Surfaces

The ancient art of sundial designing and making has produced an astonishing variety of designs, many of them ingenious and works of art. The history and a fair sample of various designs can be found in [Ro] or [Pe,Sch,SP]. The principles of working are in many cases forgotten and understood only by a very tedious reverse-engineering, often made much more difficult by wellmeant but incompetent r...

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Robert Hooke is commonly thought of as the inventor of ‘Hooke’s joint’ or the ‘universal joint’. However, it is shown that this flexible coupling (based on a four-armed cross pivoted between semicircular yokes attached to two shafts) was in fact known long before Hooke’s time but was always assumed to give an output exactly matching that of the input shaft. Hooke carefully measured the relative...

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Forward and adjoint sensitivity analysis with continuous explicit Runge - Kutta methods ⋆

We study the numerical solution of tangent linear, first, and second order adjoint models with high-order explicit, continuous Runge-Kutta methods. The approaches currently implemented in popular packages such as SUNDIALS or DASPKADJOINT are based on linear multistep methods. For adaptive time integration of nonlinear models, interpolation of the forward model solution is required during the ad...

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ژورنال

عنوان ژورنال: ACM Transactions on Mathematical Software

سال: 2005

ISSN: 0098-3500,1557-7295

DOI: 10.1145/1089014.1089020