APPLICATION OF THE LAPLACE ADOMIAN DECOMPOSITION AND IMPLICIT METHODS FOR SOLVING BURGERS' EQUATION

In this work, the modified Laplace Adomian decomposition method (LADM) is applied to solve the Burgers' equation. In addition, example that illustrate the pertinent features of this method is presented, and the results of the study is discussed. We prove the convergence of LADM applied to the Burgers' equation. Also, Burgers' equation has some discontinuous solutions because of effects of viscosity term. These discontinuities raise phenomenon of shock waves. Some explicit and implicit numerical methods have been experimented on Burgers' equation but these schemes have not been seen proper in this case because of their conditional stability and existence of viscosity term. We consider two types of box schemes and implement on Burgers' equation to get better results with no artificial wiggles.