A NEW LINEAR SCHEME FOR SOLVING THE 1-D BURGER’S EQUATION

A new model technique based on the linearization of Burger’s equation is introduced. In this paper we consider the approximate solution of the following nonlinear one dimensional Burgers’ equation. A new discretization scheme is introduced. A proof of convergence of the approximate solution is given and error estimates are derived. The numerical results obtained by the suggested technique are compared with the exact solution of the problem and also with other numerical methods. It is shown that our scheme is comparable with the others, and the numerical solution displays the expected convergence to the exact one as the mesh size is refined