scholarly journals Padé Approximation to Solve the Problems of Aerodynamics and Heat Transfer in the Boundary Layer

2020 ◽  
Author(s):  
Igor Andrianov ◽  
Anatoly Shatrov
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Asymptotic Expansions ◽  
Asymptotic Methods ◽  
Padé Approximation ◽  
Mathematical Physics ◽  
Pade Approximation ◽  
Padé Approximations ◽  
Viscous Gas ◽  
Pade Approximations

In this chapter, we describe the applications of asymptotic methods to the problems of mathematical physics and mechanics, primarily, to the solution of nonlinear singular perturbed problems. We also discuss the applications of Padé approximations for the transformation of asymptotic expansions to rational or quasi-fractional functions. The applications of the method of matching of internal and external asymptotics in the problem of boundary layer of viscous gas by means of Padé approximation are considered.

scholarly journals High-redshift cosmography: auxiliary variables versus Padé polynomials

2020 ◽  
Vol 494 (2) ◽  
pp. 2576-2590 ◽  
Author(s):  
S Capozziello ◽  
R D’Agostino ◽  
O Luongo
Keyword(s):  
High Redshift ◽  
Padé Approximation ◽  
Monte Carlo Analysis ◽  
Pade Approximation ◽  
Shift Parameter ◽  
Padé Approximations ◽  
Pade Approximations ◽  
Optimal Approach ◽  
Fifth Order ◽  
The Universe

ABSTRACT Cosmography becomes non-predictive when cosmic data span beyond the redshift limit z ≃ 1. This leads to a strong convergence issue that jeopardizes its viability. In this work, we critically compare the two main solutions of the convergence problem, i.e. the y-parametrizations of the redshift and the alternatives to Taylor expansions based on Padé series. In particular, among several possibilities, we consider two widely adopted parametrizations, namely y1 = 1−a and $y_2=\arctan (a^{-1}-1)$, being a the scale factor of the Universe. We find that the y2-parametrization performs relatively better than the y1-parametrization over the whole redshift domain. Even though y2 overcomes the issues of y1, we get that the most viable approximations of the luminosity distance dL(z) are given in terms of Padé approximations. In order to check this result by means of cosmic data, we analyse the Padé approximations up to the fifth order, and compare these series with the corresponding y-variables of the same orders. We investigate two distinct domains involving Monte Carlo analysis on the Pantheon Superovae Ia data, H(z) and shift parameter measurements. We conclude that the (2,1) Padé approximation is statistically the optimal approach to explain low- and high-redshift data, together with the fifth-order y2-parametrization. At high redshifts, the (3,2) Padé approximation cannot be fully excluded, while the (2,2) Padé one is essentially ruled out.

scholarly journals Global Padé Approximations of the Generalized Mittag-Leffler Function and its Inverse

2015 ◽  
Vol 18 (6) ◽  
Author(s):  
Caibin Zeng ◽  
Yang Quan Chen
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Padé Approximations ◽  
Pade Approximations

AbstractThis paper proposes a global Padé approximation of the generalized Mittag-Leffler function E

Padé approximations and analog computer simulations of time delays

SIMULATION ◽  
1969 ◽  
Vol 12 (6) ◽  
pp. 277-290 ◽  
Author(s):  
Per A. Holst
Keyword(s):  
Time Delays ◽  
Padé Approximation ◽  
Phase Error ◽  
Analog Computer ◽  
Rate Of Change ◽  
Step Response ◽  
Pade Approximation ◽  
Padé Approximations ◽  
Pade Approximations ◽  
Order And Type

The Padé approximations 1 of e- x are reviewed in con nection with their application in simulations of transpor tation delays (time delays) by analog computers. The approximation coefficients are specified in terms of the order of the approximations, and recurrence relation ships are established for the most common types. Analog computer circuits are given for general Padé approxima tions of any order and type, together with practical exam ples of both constant and variable transportation delay simulations. Special attention is paid to the zero-variable delay time constant, and circuits are given for this type of application. The performance of the Padé approximation circuits is discussed in terms of phase error and amplitude char acteristics for sinusoidal signals, together with rate-of- change measures in connection with step-response analy ses. Conclusions are drawn as to the order and type of Padé approximation to be selected to meet given per formance requirements. A table of Padé approximations up to the 12th order is included.

scholarly journals On the Padé and Laguerre–Tricomi–Weeks Moments Based Approximations of the Scale Function W and of the Optimal Dividends Barrier for Spectrally Negative Lévy Risk Processes

Risks ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 121
Author(s):  
Florin Avram ◽  
Andras Horváth ◽  
Serge Provost ◽  
Ulyses Solon
Keyword(s):  
Risk Model ◽  
Padé Approximation ◽  
Scale Function ◽  
Pade Approximation ◽  
Padé Approximations ◽  
Laguerre Expansions ◽  
Optimal Dividends ◽  
Pade Approximations ◽  
Heavy Tailed ◽  
Risk Processes

This paper considers the Brownian perturbed Cramér–Lundberg risk model with a dividends barrier. We study various types of Padé approximations and Laguerre expansions to compute or approximate the scale function that is necessary to optimize the dividends barrier. We experiment also with a heavy-tailed claim distribution for which we apply the so-called “shifted” Padé approximation.

Asymptotic Methods for an Infinite Slider Bearing With a Discontinuity in Film Slope

1976 ◽  
Vol 98 (3) ◽  
pp. 446-452 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima
Keyword(s):  
Boundary Layer ◽  
Film Thickness ◽  
Asymptotic Expansions ◽  
Asymptotic Expression ◽  
Asymptotic Methods ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Trailing Edge ◽  
Slider Bearings ◽  
Special Cases

The method of matched asymptotic expansions is used to develop an asymptotic expression for the pressure for large bearing numbers for the case of an infinite slider bearing with a general film thickness that has a discontinuous slope at a point. It is shown that, in addition to the boundary layer of the pressure at the trailing edge, there is also a boundary layer in the derivative of the pressure at the point of discontinuity. The corresponding load formula is also derived. The special cases of the taper-flat and taper-taper slider bearings are discussed.

Model Reduction of Transfer Functions Using a Dominant Root Method

1990 ◽  
Vol 112 (3) ◽  
pp. 547-554 ◽  
Author(s):  
J. E. Seem ◽  
S. A. Klein ◽  
W. A. Beckman ◽  
J. W. Mitchell
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Model Reduction ◽  
Transfer Functions ◽  
Linear Time ◽  
Padé Approximation ◽  
Computational Effort ◽  
Pade Approximation ◽  
Bilinear Transformation ◽  
Transfer Problems

Transfer function methods are more efficient for solving long-time transient heat transfer problems than Euler, Crank-Nicolson, or other classical techniques. Transfer functions relate the output of a linear, time-invariant system to a time series of current and past inputs, and past outputs. Inputs are modeled by a continuous, piecewise linear curve. The computational effort required to perform a simulation with transfer functions can be significantly decreased by using the Pade´ approximation and bilinear transformation to determine transfer functions with fewer coefficients. This paper presents a new model reduction method for reducing the number of coefficients in transfer functions that are used to solve heat transfer problems. There are two advantages of this method over the Pade´ approximation and bilinear transformation. First, if the original transfer function is stable, then the reduced transfer function will also be stable. Second, reduced multiple-input single-output transfer functions can be determined by this method.

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.

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