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

Abstract

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.