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Piecewise Polynomial in solving Fredholm Integral Equation of Second Kind by using Successive over Relaxation method

Piecewise Polynomial in solving Fredholm Integral Equation of Second Kind by using Successive over Relaxation method
	© 2023 by IJETT Journal
	Volume-71 Issue-2
	Year of Publication : 2023
	Author : Nor Syahida Mohamad, Jumat Sulaiman, Azali Saudi, Nur Farah Azira Zainal
	DOI : 10.14445/22315381/IJETT-V71I2P220

How to Cite?

Nor Syahida Mohamad, Jumat Sulaiman, Azali Saudi, Nur Farah Azira Zainal, "Piecewise Polynomial in solving Fredholm Integral Equation of Second Kind by using Successive over Relaxation method," International Journal of Engineering Trends and Technology, vol. 71, no. 2, pp. 165-173, 2023. Crossref, https://doi.org/10.14445/22315381/IJETT-V71I2P220

Abstract
The Gauss-Seidel and Successive over Relaxation methods are two classic methods frequently used to solve the system linear equation. This study has stated that the Gauss-Seidel method was a linear solver, and both iterative methods operated in column and row spaces, respectively. In addition, the modification of the GS method has transformed the Successive Over Relaxation (SOR) thus, has improvised the iteration process in terms of iteration size and computational time. Therefore, to prove those parameters of the iteration process, the first-order piecewise polynomial has been applied to the Fredholm integral equation of second kind (FIE) with collocation point with composited trapezoidal quadrature method in order to get the approximation equations of Fredholm integral. This paper has successfully derived an approximation equation of composited trapezoidal method with first-order piecewise polynomial through the process of discretization on the FIEs with the consideration of vertex-centered type on the domain solutions. As mentioned previously, the numerical experiment has been tested on the approximation equation of composited trapezoidal method with first-order piecewise polynomial by using the derived algorithm of Gauss-Seidel (GS) and Successive Over Relaxation (SOR). The results that have also been recorded included the Maximum absolute error (MAE) besides the iteration size (IC) and computational time (CT).

Keywords
Collocation, SOR, GS, Piecewise, Polynomial, Trapezoidal.

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