First Order Piecewise Collocation Solution of Fredholm Integral Equation Second Type Using SOR Iteration

Mohamad, Nor Syahida; Sulaiman, Jumat; Saudi, Azali; Zainal, N. F. A.

doi:10.1007/978-981-33-4069-5_32

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…Since the LS has these main features for the coefficient matrix, then the iterative methods are the most effective linear solver to seek the approximate solution of the proposed problem. Presently, there are many researchers have proposed and applied numerous iterative family such as Gauss-Seidel (GS) and successive over relaxation (SOR) iterative methods for solving LS [13]- [18]. Actually, these basic iterative methods are low in convergence rate, therefore, several researchers have modified a new variant of basic iterative methods such as preconditioned SOR (PSOR) iterative method in a way to increase the convergence rate of proposed iterative methods [19]- [21].…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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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“…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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Numerical solution of nonlinear Fredholm integral equations using Newton-PKSOR with Simpson’s 1/3

Ali,

Sulaiman,

Saudi

et al. 2024

AIP Conference Proceedings

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First Order Piecewise Collocation Solution of Fredholm Integral Equation Second Type Using SOR Iteration

Cited by 3 publications

References 10 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 Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems

Numerical solution of nonlinear Fredholm integral equations using Newton-PKSOR with Simpson’s 1/3

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