scholarly journals The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

2006 ◽  
Vol 84 (2) ◽  
pp. 121-129 ◽  
Author(s):  
T Barakat ◽  
K Abodayeh ◽  
B Abdallah ◽  
O M Al-Dossary
Keyword(s):  
Excellent Agreement ◽  
Iteration Method ◽  
Full Range ◽  
Numerical Results ◽  
Asymptotic Iteration Method ◽  
Published Data ◽  
Size Parameter ◽  
Arbitrary Complex ◽  
Parameter Values

The asymptotic iteration method is applied to calculate the angular spheroidal eigenvalues [Formula: see text] (c) with arbitrary complex size parameter c. It is shown that the numerical results obtained for [Formula: see text] (c) are all in excellent agreement with the available published data over the full range of parameter values [Formula: see text] m, and c. Some representative values of [Formula: see text] (c) for large real c are also given.PACS No.: 02.70.–c.

THE ASYMPTOTIC ITERATION METHOD FOR THE EIGENENERGIES OF THE ASYMMETRICAL QUANTUM ANHARMONIC OSCILLATOR POTENTIALS $V(x)=\sum_{j=2}^{2\alpha}A_{j}x^{j}$

2007 ◽  
Vol 22 (01) ◽  
pp. 203-212 ◽  
Author(s):  
T. BARAKAT ◽  
O. M. AL-DOSSARY
Keyword(s):  
Rate Of Convergence ◽  
Iteration Method ◽  
Anharmonic Oscillator ◽  
Full Range ◽  
Adjustable Parameter ◽  
Numerical Results ◽  
Asymptotic Iteration Method ◽  
Anharmonic Oscillators ◽  
Parameter Values

The asymptotic iteration method is used to calculate the eigenenergies for the asymmetrical quantum anharmonic oscillator potentials [Formula: see text], with (α = 2) for quartic, and (α = 3) for sextic asymmetrical quantum anharmonic oscillators. An adjustable parameter β is introduced in the method to improve its rate of convergence. Comparing the present results with the exact numerical values, and with the numerical results of the earlier works, it is found that asymptotically, this method gives accurate results over the full range of parameter values Aj.

GENERAL EIGENVALUE PROBLEMS WITH UNBOUNDED POTENTIAL FROM BELOW

2009 ◽  
Vol 24 (22) ◽  
pp. 4169-4176 ◽  
Author(s):  
A. J. SOUS ◽  
M. I. EL-KAWNI
Keyword(s):  
Iteration Method ◽  
Eigenvalue Problems ◽  
Full Range ◽  
Numerical Results ◽  
Asymptotic Iteration Method ◽  
Complete Agreement ◽  
Analytical Expression ◽  
Solvable Case ◽  
Unbounded Potential ◽  
Parameter Values

The eigenvalues of unbounded potential from below of the form [Formula: see text], has been obtained over a full range of the parameter values a and b. The calculated results are in complete agreement with exact numerical results obtained by H.-T. Cho and C.-L. Ho. Moreover, we also obtained analytical expression for En in the case when b = 0. Some new results for non-quasiexactly solvable case are presented using the asymptotic iteration method.

Any ℓ-state solutions of the Eckart potential via asymptotic iteration method

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Babatunde Falaye
Keyword(s):  
Schrödinger Equation ◽  
Excellent Agreement ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Asymptotic Iteration Method ◽  
Centrifugal Term ◽  
Energy Eigenvalues ◽  
Eckart Potential ◽  
Term Energy

AbstractThe asymptotic iteration method is employed to calculate the any ℓ-state solutions of the Schrödinger equation with the Eckart potential by proper approximation of the centrifugal term. Energy eigenvalues and corresponding eigenfunctions are obtain explicitly. The energy eigenvalues are calculated numerically for some values of ℓ and n. Our results are in excellent agreement with the findings of other methods for short potential ranges.

Investigation of the Flow and Heat Transfer around Cylinders at Low Re

2010 ◽  
Vol 156-157 ◽  
pp. 1630-1634
Author(s):  
Lei Yue ◽  
Zhi Guo Zhang ◽  
Da Kui Feng ◽  
Ashvinikumar V. Mudaliar
Keyword(s):  
Heat Transfer ◽  
Strouhal Number ◽  
Excellent Agreement ◽  
Stokes Equations ◽  
Flow Direction ◽  
Incident Angle ◽  
Numerical Results ◽  
Published Data ◽  
Square Cylinder ◽  
Flow And Heat Transfer

2-D computational analyses were conducted for unsteady viscous flow and heat transfer across cylinders of different geometries and different incident angle. Circular, square (both at 0° and 90° angles of incidence) and elliptic cylinders were examined. The calculations were performed by solving the unsteady 2-D Navier-Stokes equations at Re = 100. The calculated results produce drag and lift coefficients, as well as Strouhal number in excellent agreement with published data. Calculations for unsteady, incompressible 2-D flow around a square cylinder at incidence angle of 0° and 45° and for Reynolds number = 100 were carried out. Cycle independence and grid independence results were obtained for the Strouhal number. The results were in excellent agreement with the available experimental and numerical results. Numerical results show that the Strouhal number increases with fluid angle of incidence on the cylinder. The wake behind the cylinder is wider and more violent for a square cylinder at 45° incidence compared to a square at 0° this is due to the increase in the characteristic length in the flow direction. The present studywas carried out for a 2-D single cylinder at fixed location inside a channel for unidirectional velocity. To get more accurate results computation on 3-D geometry should be carried out.

The asymptotic iteration method applied to certain quasinormal modes and non Hermitian systems

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Okan Özer ◽  
Pinaki Roy
Keyword(s):  
Schrödinger Equation ◽  
Excellent Agreement ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Quasinormal Modes ◽  
Asymptotic Iteration Method ◽  
Exact Results

AbstractWe study the Schrödinger equation with potentials admitting quasinormal modes using the asymptotic iteration method (AIM). We also study non-Hermitian PT symmetric potentials using AIM. The spectra, in all cases, are found to be in excellent agreement with exact results.

Unsteady Numerical Analysis of Flow Across 2D Cylinder

2010 ◽  
Author(s):  
Yaling Peng ◽  
Zhiguo Zhang ◽  
Fangliang Wu ◽  
Dakui Feng
Keyword(s):  
Strouhal Number ◽  
Excellent Agreement ◽  
Incidence Angle ◽  
Flow Direction ◽  
Incident Angle ◽  
Numerical Results ◽  
Published Data ◽  
Angle Of Incidence ◽  
Square Cylinder ◽  
Navier Stokes Equation

2-D computational analyses were conducted for unsteady viscous flow across cylinders of different geometries and different incident angle. Circular, square and elliptic (both at 0° and 90° angles of incidence) cylinders were examined. The calculations were performed by solving the unsteady 2-D Navier-Stokes equation at Re = 100. The calculated results produce drag and lift coefficients, as well as Strouhal number in excellent agreement with published data. Calculations for unsteady, incompressible 2D flow around a square cylinder at incidence angle of 0° and 45° and for Reynolds number = 100 were carried out. Cycle independence and grid independence results were obtained for the Strouhal number. The results were in excellent agreement with the available experimental and numerical results. Numerical results show that the Strouhal number increases with fluid angle of incidence on the cylinder. The wake behind the cylinder is wider and more violent for a square cylinder at 45° incidence compared to a square at 0° this is due to the increase in the characteristic length in the flow direction. The Strouhal number is highest for elliptic geometry among all cylinders in this research. For the geometries elliptic at 0° at Re = 100, there is not vortex shedding behind the cylinder. This is due to dominance of inertia forces over viscous forces. The present study was carried out for a 2-D single cylinder at fixed location inside a channel for unidirectional velocity. To get more accurate results computation on 3-D geometry should be carried out.

The behaviour of heavily loaded line contacts with transverse roughness

1999 ◽  
Vol 213 (4) ◽  
pp. 309-320 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Surface Roughness ◽  
Full Range ◽  
Numerical Results ◽  
Operating Conditions ◽  
Entrainment Velocity ◽  
Original Surface ◽  
Line Contacts ◽  
Transverse Roughness ◽  
Inlet Length

In heavily loaded, piezoviscous contacts the surface roughness tends to be flattened inside the conjunction by any relative sliding of the surfaces. However, before it is flattened, the roughness affects the inlet to the contact, producing clearance variations there. These variations are then convected through the contact, at the entrainment velocity, producing a clearance distribution that differs from the original surface. The present paper explores this behaviour and establishes how the amplitude of the convected clearance varies with wavelength and operating conditions. It is shown that the primary influence is the ratio of the wavelength to the inlet length of the conjunction. Where this ratio is large, the roughness is smoothed and there is little variation in clearance under the conjunction. Where the ratio is small, significant variations in clearance may occur but the precise amplitude and phasing depend on the ratio of slide to roll velocities and on the value of a piezoviscous parameter, c. The numerical results agree closely with existing solutions but extend these to cover the full range of operating conditions.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

EIGENENERGIES FOR THE RAZAVY POTENTIAL V(x) = (ζ cosh 2x-M)2 USING THE ASYMPTOTIC ITERATION METHOD

2007 ◽  
Vol 22 (22) ◽  
pp. 1677-1684 ◽  
Author(s):  
A. J. SOUS
Keyword(s):  
Excited States ◽  
Iteration Method ◽  
Asymptotic Iteration Method ◽  
Arbitrary Parameter ◽  
Exactly Solvable

By using the asymptotic iteration method, we have calculated numerically the eigenenergies En of Razavy potential V(x) = (ζ cosh 2x-M)2. The calculated eigenenergies are identical with known values in the literature. Finally, the non-quasi-exactly solvable eigenenergies of Razavy potential for the highest excited states are numerically determined. Some new results for arbitrary parameter M also presented.

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