He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...

By using an extended ( ′ G )-expansion method, we construct the traveling wave solutions of the (2+1)dimensional Painleve integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Veselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations, where G satisfies the second order linear ordinary differential equation. By...

In this paper we derive a representation of the deterministic 3dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self-contained proof of local existence for the nonlinear sto...

Steady supersonic two-dimensional flows governed by the Navier-Stokes equations are considered. For flows past a thin body, the Oseen theory is shown to fail at large distances. An investigation of the equations bridging the linear and non-linear zones is made. From this, it follows that the resulting equations are a system of Burgers and diffusion equations. The Whitham theory is shown to resu...

‎in this paper‎, ‎we propose two preconditioned aor iterative methods to solve systems of linear equations whose coefficient matrices are z-matrix‎. ‎these methods can be considered as improvements of two previously presented ones in the literature‎. ‎finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

we introduce a rbfs mesheless method of lines that decomposes the interior and boundary centers to obtain the numerical solution of the time dependent pdes. then, the method is applied with an adaptive algorithm to obtain the numerical solution of one dimensional problem. we show that in the problems in which the solutions contain region with rapid variation, the adaptive rbfs methods are succe...

In this paper we study the asymptotic behaviour of solutions of a system of N partial differential equations. When N = 1 the equation reduces to the Burgers equation and was studied by Hopf. We consider both the inviscid and viscous case and show a new feature in the asymptotic behaviour.

In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical and engineering problems linear and nonlinear. In this article, we shall use the homotopy perturbation method (HPM) to solve some systems of partial differential equations viz. the systems of coupled Burgers’ equations in oneand twodimensions and the system of Laplace’s equation. This a...