Application of SOR iteration with nonlocal arithmetic discretization scheme for solving Burger’s equation

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

doi:10.1063/1.5054234

Cited by 7 publications

(5 citation statements)

References 14 publications

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“…where 𝐶 is lower triangular, 𝑊 is diagonal and 𝐻 is upper triangular matrices. Then, we consider ( 8) and (10) to construct the formulation of PSOR iterative method as [28]: iii. Present the approximate solution.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Methodsmentioning

confidence: 99%

“…For this reason, we avoid using such approach in order to attain low computational complexity. Therefore, we consider a method which is semi-implicit that is capable to alter any NLS into a sequence of LS [10]- [12].…”

Section: Introductionmentioning

confidence: 99%

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

Zainal

Sulaiman²,

Saudi³

et al. 2023

IJEECS

View full text Add to dashboard Cite

show abstract

“…One of the WM methods to be investigated in this paper is the Arithmetic Mean (AM) iterative method [16]. In the previous literature, the AM method and its variants have been studied and scrutinized on linear and nonlinear systems arising from a variety of scientific problems such as [17][18][19][20][21][22]. In [14,16], the numerical simulations showed that the AM method compares favorably against the existing nonstationary iterative method, particularly when the iteration matrix is strongly asymmetric.…”

Section: Preliminarymentioning

confidence: 99%

A Newton-Modified Weighted Arithmetic Mean Solution of Nonlinear Porous Medium Type Equations

et al. 2021

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The mathematical theory behind the porous medium type equation is well developed and produces many applications to the real world. The research and development of the fractional nonlinear porous medium models also progressed significantly in recent years. An efficient numerical method to solve porous medium models needs to be investigated so that the symmetry of the designed method can be extended to future fractional porous medium models. This paper contributes a new numerical method called Newton-Modified Weighted Arithmetic Mean (Newton-MOWAM). The solution of the porous medium type equation is approximated by using a finite difference method. Then, the Newton method is applied as a linearization approach to solving the system of nonlinear equations. As the system to be solved is large, high computational complexity is regulated by the MOWAM iterative method. Newton-MOWAM is formulated technically based on the matrix structure of the system. Some initial-boundary value problems with a different type of nonlinear diffusion term are presented. As a result, the Newton-MOWAM showed a significant improvement in the computation efficiency compared to the developed standard Weighted Arithmetic Mean iterative method. The analysis of efficiency, measured by the reduced number of iterations and computation time, is reported along with the convergence analysis.

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“…In addition, the successive over-relaxation iterative (SOR) method is also used in this study to solve a linear system generated from the five-point rotated similarity finite difference approximation equation. Presently, this method has been dramatically considered and exploited in a variety of applications, see [37][38][39][40][41].…”

Section: Introductionmentioning

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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Application of SOR iteration with nonlocal arithmetic discretization scheme for solving Burger’s equation

Cited by 7 publications

References 14 publications

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

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

A Newton-Modified Weighted Arithmetic Mean Solution of Nonlinear Porous Medium Type Equations

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

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