Conformal mapping, Padé approximants, and an example of flow with a significant deformation of the free boundary

2014 ◽  
Vol 25 (6) ◽  
pp. 729-747 ◽  
Author(s):  
E. A. KARABUT ◽  
A. A. KUZHUGET

A problem of plane inertial motion of an ideal incompressible fluid with a free boundary, which initially has a quadratic velocity field, is studied by semi-analytical methods. A conformal mapping of the domain occupied by the fluid onto a unit circle is sought in the form of a power series with respect to time. Summation of series is performed by using Padé approximants.

2018 ◽  
Vol 30 (2) ◽  
pp. 298-337 ◽  
Author(s):  
E. A. KARABUT ◽  
A. G. PETROV ◽  
E. N. ZHURAVLEVA

A problem from the class of unsteady plane flows of an ideal fluid with a free boundary is considered. A conformal mapping of the exterior of a unit circle onto the region occupied by the fluid is sought. The solution is constructed in the form of power series in time or Laurent series which are analytically continued with the use of Padé approximants and change of variables of a certain special type. The free boundary shape and the pressure and velocity distributions are found. Singularities of the solution are studied.


2013 ◽  
Vol 18 (3) ◽  
pp. 935-943
Author(s):  
O.D. Makinde ◽  
U.S. Mahabaleswar ◽  
N. Maheshkumar

Abstract In this paper, the Adomian decomposition method with Padé approximants are integrated to study the boundary layer flow of a conducting fluid past a linearly stretching sheet under the action of a transversely imposed magnetic field. A closed form power series solution based on Adomian polynomials is obtained for the similarity nonlinear ordinary differential equation modelling the problem. In order to satisfy the farfield condition, the Adomian power series is converted to diagonal Padé approximants and evaluated. The results obtained using ADM-Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily employed to solve a wide range of nonlinear boundary value problems


2003 ◽  
Vol 14 (04) ◽  
pp. 509-527 ◽  
Author(s):  
S. GLUZMAN ◽  
D. SORNETTE ◽  
V. I. YUKALOV

We apply the technique of self-similar exponential approximants based on successive truncations of simple continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power series. Comparison with the standard Padé approximants shows that, in general, the self-similar exponential approximants provide significantly better reconstructions.


A new proof of the theorem of de Montessus is given which does not depend upon the assumption of normality of the power series from which the Padé approximants are formed. The study is extended to sequences of approximants to double series, generalizations of Padé approximants. Several generalizations of the theorem of de Montessus to these sequences are stated and proved.


Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1869
Author(s):  
Igor Andrianov ◽  
Anatoly Shatrov

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.


1995 ◽  
Vol 06 (04) ◽  
pp. 495-501 ◽  
Author(s):  
J. FLEISCHER

In a recent paper1 a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared, a certain conformal mapping and subsequent resummation by means of Padé approximants. I present numerical examples.


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