scholarly journals An accurate solution of the Poisson equation by the Legendre Tau method

1997 ◽  
Vol 20 (4) ◽  
pp. 713-718
Author(s):  
Muhammad I. Syam
Keyword(s):  
Poisson Equation ◽  
Test Problem ◽  
Accurate Solution ◽  
Tau Method ◽  
Chebyshev Collocation Method ◽  
The Poisson Equation ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Comparison Of The Results

A new Tau method is presented for the two dimensional Poisson equation Comparison of the results for the test problemu(x,y)=sin(4πx)sin(4πy)with those computed by Haidvogel and Zang, using the matrix diagonalization method, and Dang-Vu and Delcarte, using the Chebyshev collocation method, indicates that our method would be more accurate.

CASE STUDY OF THE CONVERGENCY OF NONLINEAR PERTURBATION SERIES: MORSE–FESHBACH NONLINEAR SERIES

1999 ◽  
Vol 14 (13) ◽  
pp. 2103-2115 ◽  
Author(s):  
BISWANATH RATH
Keyword(s):  
New York ◽  
Energy Levels ◽  
Perturbation Series ◽  
Nonlinear Perturbation ◽  
Theoretical Physics ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Divergent Behavior

We study the divergent behavior of the Morse–Feshbach nonlinear perturbation series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy levels using the ground state of a quartic anharmonic oscillator (AHO) in the strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.

scholarly journals An Efficient Spectral Method to Solve Multi-Dimensional Linear Partial Different Equations Using Chebyshev Polynomials

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 90 ◽  
Author(s):  
Sahuck Oh
Keyword(s):  
Differential Equation ◽  
Inverse Method ◽  
Stokes Problem ◽  
Linear Partial Differential Equation ◽  
Helmholtz Equations ◽  
Inverse Technique ◽  
Poisson Equations ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization

We present a new method to efficiently solve a multi-dimensional linear Partial Differential Equation (PDE) called the quasi-inverse matrix diagonalization method. In the proposed method, the Chebyshev-Galerkin method is used to solve multi-dimensional PDEs spectrally. Efficient calculations are conducted by converting dense equations of systems sparse using the quasi-inverse technique and by separating coupled spectral modes using the matrix diagonalization method. When we applied the proposed method to 2-D and 3-D Poisson equations and coupled Helmholtz equations in 2-D and a Stokes problem in 3-D, the proposed method showed higher efficiency in all cases than other current methods such as the quasi-inverse method and the matrix diagonalization method in solving the multi-dimensional PDEs. Due to this efficiency of the proposed method, we believe it can be applied in various fields where multi-dimensional PDEs must be solved.

ABSORPTION OF A HYDROGENIC DONOR QUANTUM DOT WITH MAGNETIC FIELD

2010 ◽  
Vol 24 (07) ◽  
pp. 657-663 ◽  
Author(s):  
JINSHENG HUANG ◽  
JIANHUI YUAN
Keyword(s):  
Magnetic Field ◽  
Optical Properties ◽  
Quantum Dot ◽  
Optical Absorption Coefficient ◽  
Hydrogenic Donor ◽  
The Matrix ◽  
Diagonalization Method ◽  
Linear Optical Properties ◽  
Matrix Diagonalization ◽  
The Magnetic Field

An investigation of the optical properties of a hydrogenic donor in a disc-like parabolic quantum dot with magnetic field has been performed by using the matrix diagonalization method. The optical absorption coefficient between the ground (L = 0) and the first excited state (L = -1) have been examined based on the computed energies and wavefunctions. We found that the linear optical properties of the hydrogenic donor in QDs are strongly affected by the confinement strength and the magnetic field strength.

Effect of the charges of impurity on the absorption of quantum dot with magnetic field

2018 ◽  
Vol 32 (16) ◽  
pp. 1850202
Author(s):  
Jinsheng Huang ◽  
Gengxin Chen
Keyword(s):  
Magnetic Field ◽  
Quantum Dot ◽  
State Energy ◽  
Optical Absorption Coefficient ◽  
Hydrogenic Impurity ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
The Magnetic Field ◽  
Parabolic Quantum Dot

An investigation of the effect of charges of impurity on the optical properties of a hydrogenic impurity in a disk parabolic quantum dot under magnetic field has been performed by using the matrix diagonalization method. The ground state energy level becomes lower as the charges of impurity increase. The optical absorption coefficient strongly reduces with increasing charges of impurity and is strongly affected by the confinement strength, the magnetic field strength, and density of electron.

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