Analytical and numerical solutions for the nonlinear Burgers and advection-diffusion equations by using a semi-analytical iterative method

In this paper, exact solutions have been obtained for 1D, 2D and 3D nonlinear Burgers' equations and systems of equations by implementing an accurate semi-analytical method. This method, originally proposed by Temimi and Ansari and herein named TAM, proved to be efficient and reliable for solving different types of linear and nonlinear problems. This method is characterized by not requiring any restrictive assumptions for the nonlinear terms. The convergence of the method is successfully presented and mathematically proved. In addition, the advection-diffusion equation is also solved by using the TAM to demonstrate the efficiency of this method. Several examples are solved either analytically or numerically, where the accuracy of the numerical solution has been demonstrated by evaluating the absolute and relative errors to show the accuracy of the proposed method. The software used in the current work is Mathematica®10.