Taylor series revisited

From Taylor Series to Taylor Models

An 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 ...

Note Pointed Taylor Bubble Revisited

General Taylor configuration expansion revisited

The validity of a series expansion proposed previously @T. H. Jensen and M. S. Chu, Phys. Fluids 27, 2881 ~1984!# for describing general Taylor configurations of magnetized plasmas has been reexamined because an apparent paradox was realized. From analyses of simple cases which can be dealt with mostly analytically, it is concluded that the paradox is a Gibbs phenomenon, and that the series exp...

Universal Taylor series

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Perturbation approaches and Taylor series

We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choose a recent application of the HPM to a dynamic system of anisotropic elasticity.