Application of SOR Iteration with Nonlocal Arithmetic Discretization Scheme for Solving Burger's Equation

The purpose of this paper is to analyze the performance of Successive Over Relaxation (SOR) method with nonlocal arithmetic discretization scheme for solving Burger's equations. To do this matter, the proposed problems need to he discretized by using second-order implicit scheme to derive the corresponding nonlinear second order implicit finite difference approximate equation. Then, the nonlocal arithmetic discretization scheme is used to transform the corresponding nonlinear implicit approximation equation into a system of linear equations. Furthermore, numerical results of four proposed problems are also included hi order to analyze the performance of SOR method compared to Gauss-Seidel (OS) method. Based on numerical results, it can be concluded that SOR method is more efficient than GS in terms of iteration numbers and computational time.