Fourth-Order Finite Difference Approach for Numerical Solution of Burgers Equation

In this paper, we present a fourth-order finite difference method for solving nonlinear one-dimensional Burgers equation. This method is unconditionally stable, fourth-order accurate in space and second-order accurate in time. Accuracy of the scheme is demonstrated by solving a test problem, and the numerical results obtained by this method for different values of Reynolds number have been compared with the exact solution and some published numerical results. The present results are also seen to be more accurate than some available results given in the open literature. Numerical results show that the proposed method is in good agreement with the exact solutions.