scholarly journals RECONSTRUCTING GENERALIZED EXPONENTIAL LAWS BY SELF-SIMILAR EXPONENTIAL APPROXIMANTS

2003 ◽  
Vol 14 (04) ◽  
pp. 509-527 ◽  
Author(s):  
S. GLUZMAN ◽  
D. SORNETTE ◽  
V. I. YUKALOV
Keyword(s):  
Power Series ◽  
Padé Approximants ◽  
The Self ◽  
Pade Approximants ◽  
Self Similar

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.

scholarly journals Non-Perturbative Solution for Hydromagnetic Flow Over a Linearly Stretching Sheet

2013 ◽  
Vol 18 (3) ◽  
pp. 935-943
Author(s):  
O.D. Makinde ◽  
U.S. Mahabaleswar ◽  
N. Maheshkumar
Keyword(s):  
Power Series ◽  
Stretching Sheet ◽  
Adomian Decomposition Method ◽  
Padé Approximants ◽  
Power Series Solution ◽  
Nonlinear Boundary Value Problems ◽  
Pade Approximants ◽  
Adomian Decomposition ◽  
Wide Range ◽  
Perturbative Solution

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

Generalizations of the theorem of de Montessus to two-variable approximants

1975 ◽  
Vol 342 (1630) ◽  
pp. 341-372 ◽  
Keyword(s):  
Power Series ◽  
Double Series ◽  
Padé Approximants ◽  
Pade Approximants

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.

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
Keyword(s):  
Velocity Field ◽  
Free Boundary ◽  
Power Series ◽  
Conformal Mapping ◽  
Incompressible Fluid ◽  
Padé Approximants ◽  
Ideal Incompressible Fluid ◽  
Inertial Motion ◽  
Pade Approximants ◽  
Summation Of Series

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.

scholarly journals Padé Approximants, Their Properties, and Applications to Hydrodynamic Problems

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1869
Author(s):  
Igor Andrianov ◽  
Anatoly Shatrov
Keyword(s):  
Power Series ◽  
Asymptotic Analysis ◽  
Original Problem ◽  
Asymptotic Methods ◽  
Padé Approximation ◽  
Padé Approximants ◽  
Point Of View ◽  
Pade Approximation ◽  
Pade Approximants ◽  
Basic Properties

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.

Rational approximants defined from power series in N variables

1974 ◽  
Vol 336 (1607) ◽  
pp. 421-452 ◽  
Keyword(s):  
Power Series ◽  
Complex Variable ◽  
Padé Approximants ◽  
Theoretical Physics ◽  
Rational Approximants ◽  
Pade Approximants ◽  
Complex Variable Methods ◽  
Several Variables ◽  
Exclusive Sets

Rational approximants in N variables z r ( r = 1, 2, ..., N ) are defined from power series in these variables. They are generalizations of the two-variable approximants defined recently, and have the properties: ( i ) they possess symmetry between the N variables; ( ii ) they exist and are in general unique: ( iii ) if any k (< N ) variables are equated to zero, the approximants reduce to approximants in ( N — k ) variables formed from the corresponding reduced power series; in particular, if k = N — 1, they reduce to diagonal Padé approximants; ( iv ) their definition is invariant under the group of transformations z r = Aω r /(1 — B r ω r ) provided A ≠ 0, for all r = 1, 2, ..., N ; this group of homographic transformations preserves the origin z r = 0 ( r = 1, 2, ..., N ) but does not allow changes in the relative scales of the variables z r ; ( v ) an approximant formed from the reciprocal series is the reciprocal of the corresponding original approximant; ( vi ) if the series is the product of two power series in mutually exclusive sets of variables, the approximant is the product of the corresponding approximants formed from the two series; ( vii ) if the series is the sum of two power series in mutually exclusive sets of variables, the approximant is the sum of the corresponding approximants formed from the two series. Rigorous proofs of the properties ( i ) and ( iii ) to ( vii ) are given, based on complex variable methods. We discuss the possible use of the approximants in practical problems, especially in theoretical physics, and their possible importance in the theory of functions of several variables.

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