Convergence of Spectral Methods for Burgers’ Equation

1992 ◽  
Vol 29 (6) ◽  
pp. 1520-1541 ◽  
Author(s):  
Weinan E
Keyword(s):  
Spectral Methods ◽  
Burgers Equation

scholarly journals A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation

Open Physics ◽  
2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Eid Doha ◽  
Ali Bhrawy ◽  
Mohamed Abdelkawy ◽  
Ramy Hafez
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Methods ◽  
Spectral Methods ◽  
Numerical Approximation ◽  
Burgers Equation ◽  
Jacobi Polynomials ◽  
Initial Boundary ◽  
Nonlinear Ordinary Differential Equation ◽  
The Given

AbstractThis article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers’ equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers’ equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

HIGHER ORDER BURGERS EQUATION

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

Finite volume and spectral methods applied to Pb-30%TI alloy solidification

2001 ◽  
Vol 11 (PR6) ◽  
pp. Pr6-151-Pr6-159 ◽  
Author(s):  
R. Guérin ◽  
M. El Ganaoui ◽  
P. Haldenwang ◽  
P. Bontoux
Keyword(s):  
Finite Volume ◽  
Spectral Methods ◽  
Ti Alloy ◽  
Alloy Solidification

Detection of Changes in the Random Signal Properties by Spectral Methods Under the Conditions of A Priori Uncertainty

1999 ◽  
Vol 53 (9-10) ◽  
pp. 1-10
Author(s):  
V. A. Omel'chenko ◽  
V. V. Balabanov ◽  
B. M. Bezruk ◽  
Yu. N. Goloborod'ko
Keyword(s):  
Spectral Methods ◽  
A Priori ◽  
Random Signal ◽  
A Priori Uncertainty
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