AR. Haghighi - Department of Mathematics, Urmia University of Technology, Urmia, ‎Iran.
M. Shojaeifard - Department of Mathematics, Urmia University of Technology, Urmia, ‎Iran.

The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to the conventional Crank-Nicolson method, the MLCN method is an explicit and unconditionally stable method. The Adomian decomposition method includes the unknown function U (x), in which each equation is defined and solved by an infinite series of unbounded functions. Velocity parameters u in the direction of the X axis, are examined at different times with different Reynolds numbers over a fixed time step. Also the accuracy of the Adomian and the Crank-Nicolson methods at different Reynolds numbers have been studied using two examples with different initial conditions, and the Adomian decomposition method is closer to the analytical ‎method.‎

Non-linear Burgers equation, Adomian method, the modified Local Crank-Nicolson ‎method.‎