‎In this paper‎, ‎a numerical method for finding the numerical solution of the Burgers-Fisher and BURGERS' nonlinear EQUATIONS is proposed‎. ‎These EQUATIONS are very important in many physical problems such as fluid dynamics‎, ‎turbulence‎, ‎sound waves and etc‎. ‎We describe a meshless method to solve the nonlinear Burgers’ equation as a stiff equation‎. ‎In the proposed method‎, ‎we also use the exponential time differencing (ETD) method‎. ‎In this method‎, ‎the moving least squares (MLS) method is used for the spatial part and the exponential time differencing(ETD) is used for the time part‎. ‎To solve these EQUATIONS‎, ‎we use the meshless method MLS to approximate the spatial derivatives‎, ‎and then use method ETDRK4 to obtain approximate solutions‎. ‎In order to improve the possible instabilities of method ETDRK4‎, ‎Approaches have been stated‎. ‎Method MLS provided good results for these EQUATIONS due to its high flexibility and high accuracy and having a moving window‎, ‎and obtains the solution at the shock point without any false oscillations‎. ‎The method is described in detail‎, ‎and a number of computational examples are presented‎. ‎The accuracy of the proposed method is demonstrated by several test simulations‎.

In this paper, modi ed simple equation method has been applied to ob-tain generalized solutions of Burgers, Huxley EQUATIONS and combined formsof these EQUATIONS. The new exact solutions of these EQUATIONS have beenobtained. It has been shown that the proposed method provides a very e ec-tive, and powerful mathematical tool for solving nonlinear partial di erentialEQUATIONS.

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers EQUATIONS is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additionally, obtained numerical results of the cubic B-spline method are compared to trigonometric cubic B-spline method, exponential cubic Bspline method and radial basis function method. Implementation simplicity and less computational cost are the main advantages of proposed scheme compared to previous proposals.

In this paper, a new three-step method based on cubic spline will be construct to the numerical solution of a class of partial differential EQUATIONS well-known as Burgers’-Huxley and Burgers’-Fisher. As we know, the maximum order achieved using cubic spline for interpolating is O(h4), but this order is reduced when it is used for the solution of differential EQUATIONS. Here we will find an O(h6) super convergent approximation for the solution of Burgers’-Huxley and Burgers’-Fisher EQUATIONS by defining some proper end conditions and constructing a three step deferred-correction algorithm. We will discuss the convergence and error bounds of the method using Green’s function definition in details. In addition, to verify the obtained error bounds, some numerical examples will be presented. Finally, we will try to show the applicability and efficiency of the method by comparing the results with other existing methods.

In this paper we present a new approach for the study of Burgers EQUATIONS. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr " and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with in nitesimal techniques of non standard analysis.

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, analytic solutions of two-dimensional coupled Burgers’ EQUATIONS are obtained by the Homotopy analysis and the Homotopy Pade methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] Homotopy Pade technique is often independent of auxiliary parameter and this technique accelerate the convergence of the related series.