Classification of Similarity Solutions for Inviscid Burgers’ Equation

2008 ◽  
Vol 20 (1) ◽  
pp. 71-77 ◽  
Author(s):  
Mehdi Nadjafikhah
Keyword(s):  
Burgers Equation ◽  
Similarity Solutions ◽  
Inviscid Burgers Equation

scholarly journals Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hongwei Yang ◽  
Yunlong Shi ◽  
Baoshu Yin ◽  
Huanhe Dong
Keyword(s):  
Exact Solutions ◽  
Discrete Symmetries ◽  
Burgers Equation ◽  
Similarity Solutions ◽  
Group Method ◽  
Lie Point Symmetries ◽  
Lie Group Method ◽  
New Exact Solutions ◽  
Inviscid Burgers Equation ◽  
Infinitesimal Transformations

We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

On the Lie point symmetry analysis and solutions of the inviscid Burgers equation

Pramana ◽  
2011 ◽  
Vol 77 (3) ◽  
pp. 407-414 ◽  
Author(s):  
MUHAMMAD A ABDULWAHHAB ◽  
ASHFAQUE H BOKHARI ◽  
A H KARA ◽  
F D ZAMAN
Keyword(s):  
Burgers Equation ◽  
Symmetry Analysis ◽  
Point Symmetry ◽  
Inviscid Burgers Equation ◽  
Lie Point Symmetry

Classification of the similarity solutions of free Kramers equation

1995 ◽  
Vol 78 (3-4) ◽  
pp. 1139-1146 ◽  
Author(s):  
Effat A. Saied
Keyword(s):  
Similarity Solutions ◽  
Kramers Equation

A Staggered Discontinuous Galerkin Method with Local TV Regularization for the Burgers Equation

2015 ◽  
Vol 8 (4) ◽  
pp. 451-474 ◽  
Author(s):  
Hiu Ning Chan ◽  
Eric T. Chung
Keyword(s):  
Exact Solution ◽  
Numerical Solution ◽  
Discontinuous Galerkin ◽  
Numerical Approximation ◽  
Burgers Equation ◽  
Smooth Solutions ◽  
Regularization Technique ◽  
Tv Regularization ◽  
Inviscid Burgers Equation ◽  
Staggered Discontinuous Galerkin Method

AbstractThe staggered discontinuous Galerkin (SDG) method has been recently developed for the numerical approximation of partial differential equations. An important advantage of such methodology is that the numerical solution automatically satisfies some conservation properties which are also satisfied by the exact solution. In this paper, we will consider the numerical approximation of the inviscid Burgers equation by the SDG method. For smooth solutions, we prove that our SDG method has the properties of mass and energy conservation. It is well-known that extra care has to be taken at locations of shocks and discontinuities. In this respect, we propose a local total variation (TV) regularization technique to suppress the oscillations in the numerical solution. This TV regularization is only performed locally where oscillation is detected, and is thus very efficient. Therefore, the resulting scheme will preserve the mass and energy away from the shocks and the numerical solution is regularized locally near shocks. Detailed description of the method and numerical results are presented.

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