We show that the solution of the Burgers equation can be approximated in LX(R), to within 0(m~1/*(lnm)2), by a random walk method generated by 0(m) particles. The nonlinear advection term of the equation is approximated by advecting the particles in a velocity field induced by the particles. The diffusive term is approximated by adding an appropriate random perturbation to the particle position...

Burgers’ equation frequently appears in the study of turbulence theory, as well as some other scientific fields. High and low Reynolds numbers play important roles in both modeling and numerical simulation. In this paper, we apply a numerical scheme to solve a two-dimensional time-fractional Burgers equation. The key feature of the proposed method is formed by combining the discontinuous Galerk...

Stochastics and Dynamics, 4(2004),245–264. We consider the stochastic Burgers equation ∂ ∂t ψ(t, r) = ∆ψ(t, r) +∇ψ(t, r) + √ γψ(t, r)η(t, r) (1) with periodic boundary conditions, where t ≥ 0, r ∈ [0, 1], and η is some spacetime white noise. A certain Markov jump process is constructed to approximate a solution of this equation.

In this paper, we deal with both nonviscous and viscous Burgers type equations on a bounded interval. We study the global exact controllability of these equations when we have three controls: one control is the right member of the equation and is constant with respect to the space variable, the two others are the boundary values. In a first time, we are interested in nonviscous Burgers type equ...

Consider the viscous Burgers equation on a bounded interval with inhomogeneous Dirichlet boundary conditions. Following the variational framework introduced in [4], we analyze a Lyapunov functional for such equation which gives the large deviations asymptotics of a stochastic interacting particles model associated to the Burgers equation. We discuss the asymptotic behavior of this energy functi...

We discuss the recent paper by Inan and Ugurlu [Inan I.E., Ugurlu Y., Exp-function method for the exact solutions of fifth order KdV equation and modified Burgers equation, Appl. Math. Comp. 217 (2010) 1294 – 1299]. We demonstrate that all exact solutions of fifth order KdV equation and modified Burgers equation by Inan and Ugurlu are trivial solutions that are reduced to constants. Moreover, w...

Keywords: Compact schemes Finite difference method Burgers' equation Low-storage Runge–Kutta scheme a b s t r a c t A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge–Kutt...

We consider the Langevin equation describing a non-viscous Burgers fluid stochastically perturbed by uniform noise. We introduce a deterministic function that corresponds to the mean of the velocity when we keep fixed the value of the position. We study interrelations between this function and the solution of the non-perturbed Burgers equation. Especially we are interested in the property of th...

In this paper an coupled Burgers' equation is considered and then a method entitled interval finite-difference method is introduced to find the approximate interval solution of interval model in level wise cases. Finally for more illustration, the convergence theorem is confirmed and a numerical example is solved.

in this paper, modified simple equation method has been applied to ob-tain generalized solutions of burgers, huxley equations and combined forms of these equations. the new exact solutions of these equations have been obtained. it has been shown that the proposed method provides a very effective, and powerful mathematical tool for solving nonlinear partial differential equations.