As it is known, the linear rational finite difference (LRFD) method has the advantage of its excellent stability, and the Successive Over-Relaxation (SOR) method has the advantage of fast convergence rate due to the flexible choice of parameter. In this paper, in order to make full use of the advantages of LRFD and SOR methods, the composite trapezoidal (CT) quadrature scheme is combined with the 3-point linear rational finite difference (3LRFD) method (CT-3LRFD) to discretize the first-order linear Fredholm integro-differential equation and produce the approximation equation. Furthermore, the SOR method is extended to be the refinement of Successive Over-Relaxation (RSOR) method which then used to solve the numerical solution of the generated linear systems. At the same time, for the sake of comparison, the classical Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods are also introduced as the control method. In the end, through several numerical examples, the three parameters of the number of iterations, the execution time and the maximum absolute error are displayed, which fully illustrate that the RSOR method is competitive with existing GS and SOR methods in solving large dense linear system generated by the CT-3LRFD formula.
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18 November 2021
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2020 (MATHTECH 2020): Sustainable Development of Mathematics & Mathematics in Sustainability Revolution
8–10 December 2020
Penang, Malaysia
Research Article|
November 18 2021
Refinement of SOR method for the rational finite difference solution of first-order Fredholm integro-differential equations
Ming-Ming Xu;
Ming-Ming Xu
a)
1
School of Mathematics and Information Technology, Xingtai University
, 054000, Xingtai, Hebei, China
2
Faculty of Science and Natural Resources, Universiti Malaysia Sabah
, 88400 Kota Kinabalu, Sabah, Malaysia
a)Corresponding author: xmmzg@sina.com
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Jumat Sulaiman;
Jumat Sulaiman
b)
2
Faculty of Science and Natural Resources, Universiti Malaysia Sabah
, 88400 Kota Kinabalu, Sabah, Malaysia
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Labiyana Hanif Ali
Labiyana Hanif Ali
c)
2
Faculty of Science and Natural Resources, Universiti Malaysia Sabah
, 88400 Kota Kinabalu, Sabah, Malaysia
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AIP Conf. Proc. 2423, 020014 (2021)
Citation
Ming-Ming Xu, Jumat Sulaiman, Labiyana Hanif Ali; Refinement of SOR method for the rational finite difference solution of first-order Fredholm integro-differential equations. AIP Conf. Proc. 18 November 2021; 2423 (1): 020014. https://doi.org/10.1063/5.0075402
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