Haar-Sinc spectral method is used for the numerical approximation of time fractional Burgers’equations with variable and constant coefficients. The main idea in this method is using a linear discretization of time and space by combination of Haar and Sinc functions, respectively. While implementing the method, the operational matrices of the fractional integral of the fractional Haar functions are made, and by using them, an algebraic equation is obtained. Then, using the collocation method, the algebraic equation is converted into a system of equations, and after solving the system with Maple software, the numerical results of the problem is obtained. The accuracy and speed of the proposed algorithm are tested by obtaining L∞, L2 error and the convergence rate.

In this article, we propose a method for the solution of the generalized Burger– Fisher equation. The method is developed using CAS wavelets in conjunction with quasi-linearization technique. The operational matrices for the CAS wavelets are derived and constructed. Error analysis and procedure of implementation of the method are provided. We compare the results produce by present method with some well known results and show that the present method is more accurate, efficient, and applicable.

The object of this paper is to solve the so–called Modified entropy equation ¦ (x, y, z) = ¦ (x, y+z,O)+m(y+z) ¦ (O, y/y+z, z/y+z), on the positive cone of Rk, where m is a given multiplicative function on this cone. After that the regular solutions of this equation are determined. Furthermore we investigate its connection between the entropy equation and other equations, as well.

In this article, the coupled Burger’, s equation which is one of the known systems of the nonlinear parabolic partial differential equations is studied. The method presented here is based on a combination of the quintic B-spline and a high order time integration scheme known as adaptive Runge-Kutta method. First of all, the application of the new algorithm on the coupled Burger’, s equation is presented. Then, the convergence of the algorithm is studied in a theorem. Finally, to test the efficiency of the new method, coupled Burger’, s equations in literature are studied. We observed that the presented method has better accuracy and efficiency compared to the other methods in the literature.

In [1], introduce a Modified variational iteration method (MVIM) for a special kind of nonlinear differential equations. In this paper, we consider variational iteration method (VIM) and MVIM (introduced in [1]) to obtain exact solution to Fisher’s equation. It is shown in this paper the application of VIM to Fisher’s equation leads to calculation of unneeded terms and more time consumed in repeated calculations for series solutions. Therefore, we use MVIM for Fisher’s equation to overcome these disadvantages.