Application of Four-Point EGSOR Iteration with Nonlocal Arithmetic Mean Discretization Scheme for Solving Burger’s Equation

Zainal, N. F. A.; Sulaiman, Jumat; Alibubin, M. U.

doi:10.1088/1742-6596/1358/1/012051

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…As mentioned in the previous section, we developed the half-sweep successive over-relaxation (HSSOR) iteration to boost the convergence speed to solve the large-scale and sparse linear system (8). To begin with, we decomposed the coefficient matrix of the linear system (8) to obtain the formulation of the proposed iterative method that can be stated as [44][45] (9) where is the diagonal matrix of is the lower triangular matrix of is the upper triangular matrix of To derive the SOR iteration formulation, first consider the implementation of a parameter as a relaxation factor into (8) and rewrite it as .…”

Section: Half-sweep Successive Over-relaxation Iterative Methodsmentioning

confidence: 99%

A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems

Ali¹,

Sulaiman²,

Saudi³

et al. 2023

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In this paper, we transformed a two-dimensional unsteady convection-diffusion equation into a two-dimensional steady convection-diffusion equation using the similarity transformation technique. This technique can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational works since the main idea of this technique is to reduce at least one independent variable. The corresponding similarity equation is then solved numerically using an effective numerical technique, namely a new five-point rotated similarity finite difference scheme via half-sweep successive over-relaxation iteration. This work compared the performance of the proposed method with Gauss-Seidel and successive over-relaxation with the full-sweep concept. Numerical tests were carried out to obtain the performance of the proposed method using C simulation. The results revealed that the combination of the five-point rotated similarity finite difference scheme via half-sweep successive over-relaxation iteration is the most superior method in terms of the iteration number and computational time compared to all these methods. Additionally, in terms of accuracy, all three iterative methods are also comparable.

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Section: Half-sweep Successive Over-relaxation Iterative Methodsmentioning

confidence: 99%

A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems

Ali¹,

Sulaiman²,

Saudi³

et al. 2023

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show abstract

“…then, we consider the segmentation of solution domain pointed out as 𝑦 𝑖 , 𝑖 = 0,1,2, … , 𝑚 − 1, 𝑚 and 𝑡 𝑗 = 0,1,2, …. Then, the SIFD scheme is used to discretize over (2) to get the equivalent NL approximation equation expressed as [29], [30]:…”

Section: Approximation Of Burgers' Equationmentioning

confidence: 99%

Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation

Zainal

Sulaiman²,

Saudi³

et al. 2023

IJEECS

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<span lang="EN-US">This paper proposes the combination of a preconditioner applied with successive over relaxation (SOR) iterative method for solving a sparse and huge scale linear system (LS) in which its coefficient matrix is a tridiagonal matrix. The purpose for applying the preconditioner is to enhance the convergence rate of SOR iterative method. Hence, in order to examine the feasibility of the proposed iterative method which is preconditioner SOR (PSOR) iterative method, first we need to derive the approximation equation of one-dimensional (1D) Burgers’ equation through the discretization process in which the second-order implicit finite difference (SIFD) scheme together with semi-approximate (SA) approach have been applied to the proposed problem. Then, the generated LS is modified into preconditioned linear system (PLS) to construct the formulation of PSOR iterative method. Furthemore, to analyze the feasibility of PSOR iterative method compared with other point iterative methods, three examples of 1D Burgers’ equation are considered. In conclusion, the PSOR iterative method is superior than PGS iterative method. The simulation results showed that our proposed iterative method has low iteration numbers and execution time.</span>

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Semi-approximate Solution for Burgers’ Equation Using SOR Iteration

Zainal

Sulaiman

Saudi

et al. 2021

Lecture Notes in Electrical Engineering

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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.

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Application of Four-Point EGSOR Iteration with Nonlocal Arithmetic Mean Discretization Scheme for Solving Burger’s Equation

Cited by 5 publications

References 9 publications

A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems

A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems

Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation

Semi-approximate Solution for Burgers’ Equation Using SOR Iteration

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