Application of refinement successive over-relaxation (RSOR) in solving the piecewise polynomial on fredholm integral equation of the second type
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 al...
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| Format: | Article |
| Language: | English English |
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Seventh Sense Research Group
2023
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| Online Access: | https://eprints.ums.edu.my/id/eprint/38210/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/38210/2/FULL%20TEXT.pdf |
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| author | Nor Syahida Mohamad Jumat Sulaiman Azali Saudi Nur Farah Azira Zainal |
| author_facet | Nor Syahida Mohamad Jumat Sulaiman Azali Saudi Nur Farah Azira Zainal |
| author_sort | Nor Syahida Mohamad |
| collection | UMS |
| description | 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. |
| first_indexed | 2024-03-06T03:27:41Z |
| format | Article |
| id | ums.eprints-38210 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:27:41Z |
| publishDate | 2023 |
| publisher | Seventh Sense Research Group |
| record_format | dspace |
| spelling | ums.eprints-382102024-02-09T03:16:50Z https://eprints.ums.edu.my/id/eprint/38210/ Application of refinement successive over-relaxation (RSOR) in solving the piecewise polynomial on fredholm integral equation of the second type Nor Syahida Mohamad Jumat Sulaiman Azali Saudi Nur Farah Azira Zainal HD49-49.5 Crisis management. Emergency management. Inflation QC170-197 Atomic physics. Constitution and properties of matter 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. Seventh Sense Research Group 2023 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/38210/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/38210/2/FULL%20TEXT.pdf Nor Syahida Mohamad and Jumat Sulaiman and Azali Saudi and Nur Farah Azira Zainal (2023) 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, 71. pp. 1-8. ISSN 22315381, https://doi.org/10.14445/22315381/IJETT-V71I6P209 |
| spellingShingle | HD49-49.5 Crisis management. Emergency management. Inflation QC170-197 Atomic physics. Constitution and properties of matter 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 |
| title | Application of refinement successive over-relaxation (RSOR) in solving the piecewise polynomial on fredholm integral equation of the second type |
| title_full | Application of refinement successive over-relaxation (RSOR) in solving the piecewise polynomial on fredholm integral equation of the second type |
| title_fullStr | Application of refinement successive over-relaxation (RSOR) in solving the piecewise polynomial on fredholm integral equation of the second type |
| title_full_unstemmed | Application of refinement successive over-relaxation (RSOR) in solving the piecewise polynomial on fredholm integral equation of the second type |
| title_short | Application of refinement successive over-relaxation (RSOR) in solving the piecewise polynomial on fredholm integral equation of the second type |
| title_sort | application of refinement successive over relaxation rsor in solving the piecewise polynomial on fredholm integral equation of the second type |
| topic | HD49-49.5 Crisis management. Emergency management. Inflation QC170-197 Atomic physics. Constitution and properties of matter |
| url | https://eprints.ums.edu.my/id/eprint/38210/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/38210/2/FULL%20TEXT.pdf |
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