scholarly journals Numerical solutions of Burgers’ equation with random initial conditions using the Wiener chaos expansion and the Lax–Wendroff scheme

2007 ◽  
Vol 20 (5) ◽  
pp. 545-550 ◽  
Author(s):  
Hongjoong Kim
Keyword(s):  
Numerical Solutions ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Chaos Expansion ◽  
Wiener Chaos ◽  
Random Initial Conditions ◽  
Wiener Chaos Expansion

scholarly journals An efficient computational method for statistical moments of Burger's equation with random initial conditions

2006 ◽  
Vol 2006 ◽  
pp. 1-21 ◽  
Author(s):  
Hongjoong Kim
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Computational Method ◽  
Statistical Moments ◽  
Efficient Computation ◽  
Wiener Chaos ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
The Monte Carlo Method ◽  
Random Initial Conditions

The paper is concerned with efficient computation of numerical solutions to Burger's equation with random initial conditions. When the Lax-Wendroff scheme (LW) is expanded using the Wiener chaos expansion (WCE), random and deterministic effects can be separated and we obtain a system of deterministic equations with respect to Hermite-Fourier coefficients. One important property of the system is that all the statistical moments of the solution to the Burger's equation can be computed using the solution of the system only. Thus LW with WCE presents an alternative to computing moments by the Monte Carlo method (MC). It has been numerically demonstrated that LW with WCE approach is equally accurate but substantially faster than MC at least for certain classes of initial conditions.

scholarly journals Burgers' turbulence problem with linear or quadratic external potential

2005 ◽  
Vol 42 (02) ◽  
pp. 550-565 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
N. N. Leonenko
Keyword(s):  
Burgers Equation ◽  
Initial Conditions ◽  
External Potential ◽  
Limit Laws ◽  
Random Initial Conditions ◽  
Burgers Turbulence

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.

New Travelling Wave Solutions of Burgers Equation with Finite Transport Memory

2010 ◽  
Vol 65 (8-9) ◽  
pp. 633-640 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun ◽  
Jonu Lee
Keyword(s):  
Evolution Equations ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Diffusion Processes ◽  
Initial Conditions ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Wide Range ◽  
Finite Memory

The nonlinear evolution equations with finite memory have a wide range of applications in science and engineering. The Burgers equation with finite memory transport (time-delayed) describes convection-diffusion processes. In this paper, we establish the new solitary wave solutions for the time-delayed Burgers equation. The extended tanh method and the exp-function method have been employed to reveal these new solutions. Further, we have calculated the numerical solutions of the time-delayed Burgers equation with initial conditions by using the homotopy perturbation method (HPM). Our results show that the extended tanh and exp-function methods are very effective in finding exact solutions of the considered problem and HPM is very powerful in finding numerical solutions with good accuracy for nonlinear partial differential equations without any need of transformation or perturbation

Sign in / Sign up

Export Citation Format

Share Document