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The main objective for this study is to examine the efficiency of block iterative method namely Four-Point Explicit Group Successive Over Relaxation (4EGSOR) iterative method. The nonlinear Burger’s equation is then solved through the application of nonlocal arithmetic mean discretization (AMD) scheme to form a linear system. Next, to scrutinize the efficiency of 4EGSOR with Gauss-Seidel (GS) and Successive Over Relaxation (SOR) iterative methods, the numerical experiments for four proposed problems are being considered. By referring to the numerical results obtained, we concluded that 4EGSOR is more superior than GS and SOR iterative methods in aspects of number of iterations and execution time.

We evaluate the first-order approximation solution piecewise by firstorder polynomial collocation with Quadrature scheme on second-type Fredholm integral equations. This discretization derived the formulation to solve the first order piecewise approximation equation in which the linear system was built. The SOR method was described as a linear solver in which its formulation was constructed and applied in this study. In order to obtain the approximation solutions, the combination of SOR iterative method with the first-order piecewise polynomial by collocation with quadrature scheme has shown that performance of SOR method is superior than Jacobi method in terms of number of iterations and time of completion.

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In this article,we propose semi-approximate approach in finding a solution of Burgers' equationwhich is one of the partial differential equations (PDEs).Without using the Newton method for linearization, we derive the approximation equation of the proposed problem by using second-order implicit scheme together with the semi-approximate approach. Then this approximation equation leads a huge scale and sparse linear system. Having this linear system, the Successive Overrelaxation (SOR) iteration will be performed as a linear solver.The formulation and execution of SOR iteration are included in this paper. This paper proposed four examples of Burgers' equations to determine the performance of the suggested method.The test results discovered that the SOR iteration is more effective than GS iteration with less time of execution and minimum iteration numbers.