Application of Refinement Successive Over-Relaxation (RSOR) in Solving the Piecewise Polynomial on Fredholm Integral Equation of the Second Type

Application of Refinement Successive Over-Relaxation (RSOR) in Solving the Piecewise Polynomial on Fredholm Integral Equation of the Second Type
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© 2023 by IJETT Journal
Volume-71 Issue-6
Year of Publication : 2023
Author : Nor Syahida Mohamad, Jumat Sulaiman, Azali Saudi, Nur Farah Azira Zainal
DOI : 10.14445/22315381/IJETT-V71I6P209

How to Cite?

Nor Syahida Mohamad, Jumat Sulaiman, Azali Saudi, Nur Farah Azira Zainal, "Application of Refinement Successive Over-Relaxation (RSOR) in Solving the Piecewise Polynomial on Fredholm Integral Equation of the Second Type ," International Journal of Engineering Trends and Technology, vol. 71, no. 6, pp. 75-82, 2023. Crossref, https://doi.org/10.14445/22315381/IJETT-V71I6P209

Abstract
This paper establishes an effective and reliable algorithm for solving the second type of FIE based on the first-order piecewise polynomial and the first-order quadrature method. The algorithm, which is called Composite Trapezium (CT), is generally used to discretize any integral term. This paper also aims to derive a Composite Trapezium (CT) with first-order piecewise polynomial and first-order quadrature linear collocation approximation equation generated from the discretization process of the proposed problem by considering the distribution of node points with vertex-centered. Accordingly, we built a system of CT linear collocation approximation equations using collocation node points over the approximation equation for linear collocation. The coefficient matrix is large and dense. In addition, this research also considered the effective Refinement Successive Over-Relaxation (RSOR) algorithm to obtain the piecewise linear collocation solution of this linear problem. In order to test the proposed iterative methods, three tested examples were solved. The results were subsequently obtained based on three parameters, including the iterations (I), execution period (s), and the maximum absolute error, which was all recorded and further compared with two iterations, SOR and RSOR.

Keywords
Piecewise, Collocation, Successive Over-Relaxation (SOR) method, and Refinement Successive Over-Relaxation (RSOR) method.

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