On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Burgers' Equation

ABSTRACT

In this paper, we present two methods for finding solutions to the one-dimensional nonlinear Burgers’ equation. The first method is an analytical one, which is based on the tanh – function method. The second method is based on the Adomian decomposition method where two approaches are introduced. The first approach considers the use of the initial condition while the other considers the use of the boundary conditions. The accuracy of the proposed numerical method is demonstrated by two test problems. The obtained results are presented and compared with the exact solution. The numerical results are found in good agreement with the exact solution in case of using the initial conditions and an acceptable accuracy for the case of using the boundary conditions. Finally, the results are presented graphically.

Keywords:

Adomian decomposition Method, tanh –function Method, nonlinear Burgers’ equation, analytical solution, accuracy.