Numerical solutions of time and space fractional coupled Burgers equations using time-space Chebyshev pseudospectral method

2020 ◽  
Author(s):  
Avinash K. Mittal ◽  
Lokendra K. Balyan
Keyword(s):  
Numerical Solutions ◽  
Pseudospectral Method ◽  
Time And Space ◽  
Chebyshev Pseudospectral Method ◽  
Burgers Equations ◽  
Time Space ◽  
Chebyshev Pseudospectral

scholarly journals Spectrally accurate approximate solutions and convergence analysis of fractional Burgers’ equation

2020 ◽  
Vol 9 (3) ◽  
pp. 633-644
Author(s):  
A. K. Mittal
Keyword(s):  
Numerical Solutions ◽  
Burgers Equation ◽  
Numerical Technique ◽  
Time Derivative ◽  
Pseudospectral Method ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Time And Space ◽  
Time Space ◽  
Coupled Burgers Equation

Abstract In this paper, a new numerical technique implements on the time-space pseudospectral method to approximate the numerical solutions of nonlinear time- and space-fractional coupled Burgers’ equation. This technique is based on orthogonal Chebyshev polynomial function and discretizes using Chebyshev–Gauss–Lobbato (CGL) points. Caputo–Riemann–Liouville fractional derivative formula is used to illustrate the fractional derivatives matrix at CGL points. Using the derivatives matrices, the given problem is reduced to a system of nonlinear algebraic equations. These equations can be solved using Newton–Raphson method. Two model examples of time- and space-fractional coupled Burgers’ equation are tested for a set of fractional space and time derivative order. The figures and tables show the significant features, effectiveness, and good accuracy of the proposed method.

scholarly journals The Rational Third-Kind Chebyshev Pseudospectral Method for the Solution of the Thomas-Fermi Equation over Infinite Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Majid Tavassoli Kajani ◽  
Adem Kılıçman ◽  
Mohammad Maleki
Keyword(s):  
Numerical Solutions ◽  
Pseudospectral Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Collocation Methods ◽  
Infinite Interval ◽  
Algebraic Equations ◽  
Chebyshev Pseudospectral Method ◽  
Thomas Fermi ◽  
Present Solution ◽  
Chebyshev Pseudospectral

We propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on the rational third-kind Chebyshev pseudospectral method that is indeed a combination of Tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. Comparison with some numerical solutions shows that the present solution is highly accurate.

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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