Numerical solution of SOR iterative method for fuzzy Fredholm integral equations of second kind

Ali, Labiyana Hanif; Sulaiman, Jumat; Hashim, Siti Rahayu Mohd

doi:10.1063/1.5054215

Cited by 4 publications

(1 citation statement)

References 8 publications

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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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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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Application of Newton-GS Iterative Method with Second-Order Quadrature Scheme in Solving Nonlinear Fredholm Integral Equations

Ali

Sulaiman

Saudi

et al. 2021

Proceedings of the 6th International Conference on Fundamental and Applied Sciences

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Newton-SOR with Quadrature Scheme for Solving Nonlinear Fredholm Integral Equations

Ali

Sulaiman

Saudi

et al. 2021

Lecture Notes in Electrical Engineering

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This paper presents a numerical method of Newton Successive Over-Relaxation (NSOR) iteration with quadrature scheme to approximate the solution of nonlinear Fredholm integral equations. Here, the quadrature scheme is used to derive the approximation equations of nonlinear Fredholm integral equations in order to develop a system of nonlinear equations.NSOR consists of two parts. In the first part, Newton's method is used to linearize the developed system of nonlinear equations. Then, in the second part, SOR iteration is used to solve the corresponding system of linear equations to get the approximate solution. In order to validate the performance of the proposed method, Newton-Jacobi (NJacobi) and Newton-Gauss-Seidel (NGS) are used as the reference methods to perform the comparative analysis. Also, some numerical examples are presented to illustrate the validity of the NSOR.

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Numerical solution of SOR iterative method for fuzzy Fredholm integral equations of second kind

Cited by 4 publications

References 8 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

Application of Newton-GS Iterative Method with Second-Order Quadrature Scheme in Solving Nonlinear Fredholm Integral Equations

Newton-SOR with Quadrature Scheme for Solving Nonlinear Fredholm Integral Equations

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