Fourier spectral approximation for generalized time fractional Burgers equation

2022 ◽  
Author(s):  
Li Chen ◽  
Shujuan Lü
Keyword(s):  
Burgers Equation ◽  
Spectral Approximation ◽  
Generalized Time

scholarly journals Improved Fractional Subequation Method and Exact Solutions to Fractional Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jun Jiang ◽  
Yuqiang Feng ◽  
Shougui Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Burgers Equation ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Biological Population ◽  
Regularized Long Wave Equation ◽  
Generalized Time

In this paper, the improved fractional subequation method is applied to establish the exact solutions for some nonlinear fractional partial differential equations. Solutions to the generalized time fractional biological population model, the generalized time fractional compound KdV-Burgers equation, the space-time fractional regularized long-wave equation, and the (3+1)-space-time fractional Zakharov-Kuznetsov equation are obtained, respectively.

scholarly journals Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dumitru Vieru ◽  
Constantin Fetecau ◽  
Nehad Ali Shah ◽  
Jae Dong Chung
Keyword(s):  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Variable Coefficients ◽  
Time Variable ◽  
Integral Representations ◽  
Finite Difference Approximations ◽  
Generalized Time ◽  
Two Parameter ◽  
Numerical Approaches

The generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. The classical Burgers equation is generalized by considering the generalized Atangana-Baleanu time-fractional derivative. The studied model contains as particular cases the Burgers equation with Atangana-Baleanu, Caputo-Fabrizio, and Caputo time-fractional derivatives. A numerical scheme, based on the finite-difference approximations and some integral representations of the two-parameter Mittag-Leffler functions, has been developed. Numerical solutions of a particular problem with initial and boundary values are determined by employing the proposed method. The numerical results are plotted to compare solutions corresponding to the problems with time-fractional derivatives with different kernels.

scholarly journals Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

2021 ◽  
Vol 54 (1) ◽  
pp. 436-451
Author(s):  
Adel R. Hadhoud ◽  
Faisal E. Abd Alaal ◽  
Ayman A. Abdelaziz ◽  
Taha Radwan
Keyword(s):  
Burgers Equation ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Spline Collocation ◽  
Von Neumann ◽  
B Spline ◽  
Stability Examination ◽  
The Mean ◽  
The Stability ◽  
Generalized Time

Abstract In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.

scholarly journals The generalized Burgers equation with and without a time delay

2004 ◽  
Vol 2004 (1) ◽  
pp. 73-96 ◽  
Author(s):  
Nejib Smaoui ◽  
Mona Mekkaoui
Keyword(s):  
Time Delay ◽  
Function Method ◽  
Burgers Equation ◽  
Pseudospectral Method ◽  
Steady State Solution ◽  
Generalized Burgers Equation ◽  
Lyapunov Function Method ◽  
Exponentially Stable ◽  
T Tau ◽  
Generalized Time

We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut=vuxx−uux+u+h(x), 0<x<2π, t>0, u(0,t)=u(2π,t), u(x,0)=u0(x), a Lyapunov function method is used to show boundedness and uniqueness of a steady state solution and global stability of the equation. As for the generalized time-delayed Burgers equation, that is, ut(x,t)=vuxx(x,t)−u(x,t−τ)ux(x,t)+u(x,t), 0<x<2π, t>0, u(0,t)=u(2π,t), t>0, u(x,s)=u0(x,s), 0<x<2π, −τ≤s≤0, we show that the equation is exponentially stable under small delays. Using a pseudospectral method, we present some numerical results illustrating and reinforcing the analytical results.

HIGHER ORDER BURGERS EQUATION

1986 ◽  
Vol 6 (3) ◽  
pp. 353-360 ◽  
Author(s):  
Mingliang Wang
Keyword(s):  
Burgers Equation ◽  
Higher Order
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