On a finite difference scheme for Burgers’ equation

In this paper we study properties of numerical solutions of Burger’s equation. Burgers’ equation is reduced to the heat equation on which we apply the Douglas finite difference scheme. The method is shown to be unconditionally stable, fourth order accurate in space and second order accurate in time. Two test problems are used to validate the algorithm. Numerical solutions for various values of viscosity are calculated and it is concluded that the proposed method performs well.