Fourier pseudospectral method for fractional stationary Schrödinger equation

2021 ◽  
Vol 165 ◽  
pp. 137-151 ◽  
Author(s):  
Yin Yang ◽  
Xueyang Li ◽  
Aiguo Xiao
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Pseudospectral Method ◽  
Stationary Schrödinger Equation ◽  
Fourier Pseudospectral Method ◽  
Fourier Pseudospectral

scholarly journals Convergent Analysis of Energy Conservative Algorithm for the Nonlinear Schrödinger Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Lv Zhong-Quan ◽  
Gong Yue-Zheng ◽  
Wang Yu-Shun
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Pseudospectral Method ◽  
Field Method ◽  
Nonlinear Schrodinger Equation ◽  
Fourier Pseudospectral Method ◽  
Nonlinear Schrödinger ◽  
Vector Field Method ◽  
Energy Conservation Law

Using average vector field method in time and Fourier pseudospectral method in space, we obtain an energy-preserving scheme for the nonlinear Schrödinger equation. We prove that the proposed method conserves the discrete global energy exactly. A deduction argument is used to prove that the numerical solution is convergent to the exact solution in discreteL2norm. Some numerical results are reported to illustrate the efficiency of the numerical scheme in preserving the energy conservation law.

scholarly journals Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jae-Young Choi ◽  
Dong Kyun Im ◽  
Jangho Park ◽  
Seongim Choi
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Accurate Method ◽  
Spectral Approach ◽  
Fourier Pseudospectral Method ◽  
Chebyshev Pseudospectral Method ◽  
Fourier Pseudospectral ◽  
Chebyshev Pseudospectral ◽  
Good Agreement

A mapped Chebyshev pseudospectral method is extended to solve three-dimensional unsteady flow problems. As the classical Chebyshev spectral approach can lead to numerical instabilities due to ill conditioning of the spectral matrix, the Chebyshev points are evenly redistributed over the domain by an inverse sine mapping function. The mapped Chebyshev pseudospectral method can be used as an alternative time-spectral approach that uses a Chebyshev collocation operator to approximate the time derivative terms in the unsteady flow governing equations, and the method can make general applications to both nonperiodic and periodic problems. In this study, the mapped Chebyshev pseudospectral method is employed to solve three-dimensional periodic problem to verify the spectral accuracy and computational efficiency with those of the Fourier pseudospectral method and the time-accurate method. The results show a good agreement with both of the Fourier pseudospectral method and the time-accurate method. The flow solutions also demonstrate a good agreement with the experimental data. Similar to the Fourier pseudospectral method, the mapped Chebyshev pseudospectral method approximates the unsteady flow solutions with a precise accuracy at a considerably effective computational cost compared to the conventional time-accurate method.

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