Higher-order accurate finite-difference schemes for solving the unsteady Burgers’ equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented. The unsteady Burgers’ equation belongs to a few nonlinear partial differential equations which has an exact solution, and it allows one to compare the numerical solution with the exact one, and the properti...

The “t-model” for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dimensions. The model was first derived in a statistical mechanics context, but here we analyze it purely as a numerical tool and prove its convergence. In the Burgers case the model captures the rate of decay exactly, a...

The "t-model" for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dimensions. The model was first derived in a statistical mechanics context, but here we analyze it purely as a numerical tool and prove its convergence. In the Burgers case, the model captures the rate of decay exactly, ...

We proposed a higher-order accurate explicit finite-difference scheme for solving the two-dimensional heat equation. It has a fourth-order approximation in the space variables, and a secondorder approximation in the time variable. As an application, we developed the proposed numerical scheme for solving a numerical solution of the two-dimensional coupled Burgers’ equations. The main advantages ...

We study the problem of global exponential stabilization original Burgers' equations and equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions controlled are steering a concrete solution non-controlled system as $t\rightarrow \infty$ an rate.

A stochastic representation of the dynamics of the Burger's turbulence model and of the two{dimensional turbulence is developed. The random velocity eld is regarded as a multivariate stochastic Markov process deened by a master equation. It is shown that Burgers' equation and the two{dimensional Navier{Stokes equation are obtained as the macroscopic equations for the averages of the underlying ...