Fourier-Chebyshev pseudospectral method for two-dimensional vorticity equation

1993 ◽  
Vol 66 (1) ◽  
pp. 329-346 ◽  
Author(s):  
Ben-yu Guo ◽  
Jian Li
Keyword(s):  
Pseudospectral Method ◽  
Vorticity Equation ◽  
Two Dimensional ◽  
Chebyshev Pseudospectral Method ◽  
Chebyshev Pseudospectral

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.

scholarly journals Numerical Analysis of the Fractional-Order Nonlinear System of Volterra Integro-Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Pongsakorn Sunthrayuth ◽  
Roman Ullah ◽  
Adnan Khan ◽  
Rasool Shah ◽  
Jeevan Kafle ◽  
...  
Keyword(s):  
Exact Solution ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Pseudospectral Method ◽  
Science And Engineering ◽  
Volterra Type ◽  
Chebyshev Pseudospectral Method ◽  
Physical Problems ◽  
Chebyshev Pseudospectral ◽  
Fractional Order Nonlinear System

This paper presents the nonlinear systems of Volterra-type fractional integro-differential equation solutions through a Chebyshev pseudospectral method. The proposed method is based on the Caputo fractional derivative. The results that we get show the accuracy and reliability of the present method. Different nonlinear systems have been solved; the solutions that we get are compared with other methods and the exact solution. Also, from the presented figures, it is easy to conclude that the CPM error converges quickly as compared to other methods. Comparing the exact solution and other techniques reveals that the Chebyshev pseudospectral method has a higher degree of accuracy and converges quickly towards the exact solution. Moreover, it is easy to implement the suggested method for solving fractional-order linear and nonlinear physical problems related to science and engineering.

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