Padé Approximants, Their Properties, and Applications to Hydrodynamic Problems

Symmetry, vol. 13, pp. 1869

Abstract

This paper is devoted to an overview of the basic properties of the Padé transformation and its generalizations. The merits and limitations of the described approaches are discussed. Particular attention is paid to the application of Padé approximants in the mechanics of liquids and gases. One of the disadvantages of asymptotic methods is that the standard ansatz in the form of a power series in some parameter usually does not reflect the symmetry of the original problem. The search for asymptotic ansatzes that adequately take into account this symmetry has become one of the most important problems of asymptotic analysis. The most developed technique from this point of view is the Padé approximation.

Authors 2

1. Igor V. Andrianov corresponding Aachen chair Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Chair and Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, D-52062 Aachen, Germany

2. A. V. Shatrov

   Vyatka State University · Kirov State Medical Academy

   Affiliation as printed

   Department of Physics and Medical Informatics, Kirov State Medical University, Karl Marx 112, RU-610000 Kirov, Russia

   Institute of Mathematics and Information Systems, Vyatka State University, Moskovskaya 36, RU-610000 Kirov, Russia