scholarly journals New solutions for the one-dimensional nonconservative inviscid Burgers equation

2006 ◽  
Vol 317 (2) ◽  
pp. 496-509 ◽  
Author(s):  
C.O.R. Sarrico
Keyword(s):  
Burgers Equation ◽  
One Dimensional ◽  
Inviscid Burgers Equation ◽  
The One

scholarly journals Jin–Xin relaxation method used to solve the one-dimensional inviscid Burgers equation

2017 ◽  
Vol 856 ◽  
pp. 012007 ◽  
Author(s):  
Sudi Mungkasi ◽  
Bernadeta Wuri Harini ◽  
Leo Hari Wiryanto
Keyword(s):  
Burgers Equation ◽  
Relaxation Method ◽  
One Dimensional ◽  
Inviscid Burgers Equation ◽  
The One

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Exact statistical properties of the Burgers equation

2000 ◽  
Vol 417 ◽  
pp. 323-349 ◽  
Author(s):  
L. FRACHEBOURG ◽  
Ph. A. MARTIN
Keyword(s):  
White Noise ◽  
Large Distance ◽  
Burgers Equation ◽  
Higher Order ◽  
Statistical Properties ◽  
Inviscid Limit ◽  
Initial Condition ◽  
Spatial Correlations ◽  
One Dimensional ◽  
The One

The one-dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behaviour of spatial correlations of the field is determined. Since higher-order distributions factorize in terms of the one- and two- point functions, our analysis provides an explicit and complete statistical description of this problem.

Space-Time Chebyshev Pseudospectral Method for Burgers Equation

2013 ◽  
Vol 475-476 ◽  
pp. 1075-1078
Author(s):  
Jia Chun Liu ◽  
Xiao Hui Qian
Keyword(s):  
Burgers Equation ◽  
Dimensional Space ◽  
Pseudospectral Method ◽  
High Accuracy ◽  
Space Time ◽  
Numerical Results ◽  
One Dimensional ◽  
Chebyshev Pseudospectral Method ◽  
The One ◽  
Chebyshev Pseudospectral

In this paper, we present a new method for solving of the one dimensional Burgers equation, that is the space-time Chebyshev pseudospectral method. Firstly, we discretize the Burgers equation in one dimensional space with Chebyshev pseudospectral method. Finally, numerical results obtained by this way are compared with the exact solution to show the efficiency of the method. The numerical results demonstrate high accuracy and stability of this method.

scholarly journals Computer modeling system for the numerical solution of the one-dimensional non-stationary Burgers’ equation

2019 ◽  
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Computer Modeling ◽  
Burgers Equation ◽  
Boundary Value ◽  
Three Dimensional ◽  
Benchmark Problems ◽  
One Dimensional ◽  
Radial Basis ◽  
The One

The computer modeling system for numerical solution of the nonlinear one-dimensional non-stationary Burgers’ equation is described. The numerical solution of the Burgers’ equation is obtained by a meshless scheme using the method of partial solutions and radial basis functions. Time discretization of the one-dimensional Burgers’ equation is obtained by the generalized trapezoidal method (θ-scheme). The inverse multiquadric function is used as radial basis functions in the computer modeling system. The computer modeling system allows setting the initial conditions and boundary conditions as well as setting the source function as a coordinate- and time-dependent function for solving partial differential equation. A computer modeling system allows setting such parameters as the domain of the boundary-value problem, number of interpolation nodes, the time interval of non-stationary boundary-value problem, the time step size, the shape parameter of the radial basis function, and coefficients in the Burgers’ equation. The solution of the nonlinear one-dimensional non-stationary Burgers’ equation is visualized as a three-dimensional surface plot in the computer modeling system. The computer modeling system allows visualizing the solution of the boundary-value problem at chosen time steps as three-dimensional plots. The computational effectiveness of the computer modeling system is demonstrated by solving two benchmark problems. For solved benchmark problems, the average relative error, the average absolute error, and the maximum error have been calculated.

scholarly journals On the Numerical Solution of One-Dimensional Nonlinear Nonhomogeneous Burgers’ Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Maryam Sarboland ◽  
Azim Aminataei
Keyword(s):  
Numerical Solutions ◽  
Burgers Equation ◽  
Meshfree Methods ◽  
Radial Basis Function Networks ◽  
One Dimensional ◽  
Temporal Derivative ◽  
Spatial Derivatives ◽  
The Stability ◽  
The One ◽  
Nonlinear Nature

The nonlinear Burgers’ equation is a simple form of Navier-Stocks equation. The nonlinear nature of Burgers’ equation has been exploited as a useful prototype differential equation for modeling many phenomena. This paper proposes two meshfree methods for solving the one-dimensional nonlinear nonhomogeneous Burgers’ equation. These methods are based on the multiquadric (MQ) quasi-interpolation operatorℒ𝒲2and direct and indirect radial basis function networks (RBFNs) schemes. In the present schemes, the Taylors series expansion is used to discretize the temporal derivative and the quasi-interpolation is used to approximate the solution function and its spatial derivatives. In order to show the efficiency of the present methods, several experiments are considered. Our numerical solutions are compared with the analytical solutions as well as the results of other numerical schemes. Furthermore, the stability analysis of the methods is surveyed. It can be easily seen that the proposed methods are efficient, robust, and reliable for solving Burgers’ equation.

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