Extending the Range of Validity for Asymptotic Energy Expansion Method by Padé Approximation

2014 ◽  
Vol 73 (3) ◽  
pp. 383-392
Author(s):  
Thilagarajah Mathanaranjan ◽  
Asiri Nanayakkara
Keyword(s):  
Padé Approximation ◽  
Expansion Method ◽  
Pade Approximation ◽  
Asymptotic Energy ◽  
Energy Expansion

A new asymptotic energy expansion method

2001 ◽  
Vol 289 (1-2) ◽  
pp. 39-43 ◽  
Author(s):  
Asiri Nanayakkara
Keyword(s):  
Expansion Method ◽  
Asymptotic Energy ◽  
Energy Expansion

Asymptotic behavior of eigen energies of non-Hermitian cubic polynomial systems

2007 ◽  
Vol 85 (12) ◽  
pp. 1473-1480 ◽  
Author(s):  
A Nanayakkara
Keyword(s):  
Asymptotic Behavior ◽  
Polynomial System ◽  
Expansion Method ◽  
Polynomial Systems ◽  
Level Spacing ◽  
Spacing Distribution ◽  
Cubic Polynomial ◽  
Asymptotic Energy ◽  
04.20 Jb ◽  
Energy Expansion

The asymptotic behavior of the eigenvalues of a non-Hermitian cubic polynomial system H = (P2/2) + µx3 + ax2 + bx, where µ, a, and b are constant parameters that can be either real or complex, is studied by extending the asymptotic energy expansion method, which has been developed for even degree polynomial systems. Both the complex and the real eigenvalues of the above system are obtained using the asymptotic energy expansion. Quantum eigen energies obtained by the above method are found to be in excellent agreement with the exact eigenvalues. Using the asymptotic energy expansion, analytic expressions for both level spacing distribution and the density of states are derived for the above cubic system. When µ = i, a is real, and b is pure imaginary, it was found that asymptotic energy level spacing increases with the coupling strength a for positive a while it decreases for negative a. PACS Nos.: 03.65.Ge, 04.20.Jb, 03.65.Sq, 02.30.Mv, 05.45

scholarly journals Hybrid Pade´-Galerkin Technique for Differential Equations

1993 ◽  
Vol 46 (11S) ◽  
pp. S255-S265
Author(s):  
James F. Geer ◽  
Carl M. Andersen
Keyword(s):  
Differential Equations ◽  
Padé Approximation ◽  
Galerkin Approximation ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Pade Approximation ◽  
Unknown Parameters ◽  
Regular Perturbation ◽  
Analysis Technique ◽  
Governing Differential Equation

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade´ expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter ε associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade´ approximation in the form of a rational function in the parameter ε. In the third step, the various powers of ε which appear in the Pade´ approximation are replaced by new (unknown) parameters {δj}. These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade´ approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Modeling of Rails Expressed using Pade Approximation Considering Frequency Dependent Effect

2017 ◽  
Vol 137 (2) ◽  
pp. 147-153
Author(s):  
Akinori Hori ◽  
Hiroki Tanaka ◽  
Yuichiro Hayakawa ◽  
Hiroshi Shida ◽  
Keiji Kawahara ◽  
...  
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Frequency Dependent ◽  
Dependent Effect

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

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