Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach
This paper examines two-stage iterative methods, specifically the Geometric Mean (GM) method and its variants, for solving dense linear systems associated with first-kind Fredholm integral equations with semi-smooth kernels. These equations, characterised by ill-posedness and sensitivity to input pe...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier Ltd
2024
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| Online Access: | http://umpir.ump.edu.my/id/eprint/43051/ http://umpir.ump.edu.my/id/eprint/43051/1/Numerical%20solution%20of%20first%20kind%20Fredholm%20integral%20equations%20with%20semi-smooth%20kernel.pdf |
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| author | Muthuvalu, Mohana Sundaram Nor Aida Zuraimi, Md Noar Harry, Setiawan Isman, Kurniawan Momani, Shaher |
| author_facet | Muthuvalu, Mohana Sundaram Nor Aida Zuraimi, Md Noar Harry, Setiawan Isman, Kurniawan Momani, Shaher |
| author_sort | Muthuvalu, Mohana Sundaram |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | This paper examines two-stage iterative methods, specifically the Geometric Mean (GM) method and its variants, for solving dense linear systems associated with first-kind Fredholm integral equations with semi-smooth kernels. These equations, characterised by ill-posedness and sensitivity to input perturbations, are discretised using a composite closed Newton-Cotes quadrature scheme. The study evaluates the computational performance and accuracy of the standard GM method, also referred to as the Full-Sweep Geometric Mean (FSGM), in comparison with the Half-Sweep Geometric Mean (HSGM) and Quarter-Sweep Geometric Mean (QSGM) methods. Numerical experiments demonstrate significant reductions in computational complexity and execution time while maintaining high solution accuracy. The QSGM method achieves the best performance among the tested methods, highlighting its effectiveness in addressing computational challenges associated with first-kind Fredholm integral equations. |
| first_indexed | 2025-11-15T03:50:05Z |
| format | Article |
| id | ump-43051 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T03:50:05Z |
| publishDate | 2024 |
| publisher | Elsevier Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-430512024-12-09T01:34:21Z http://umpir.ump.edu.my/id/eprint/43051/ Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach Muthuvalu, Mohana Sundaram Nor Aida Zuraimi, Md Noar Harry, Setiawan Isman, Kurniawan Momani, Shaher QA Mathematics This paper examines two-stage iterative methods, specifically the Geometric Mean (GM) method and its variants, for solving dense linear systems associated with first-kind Fredholm integral equations with semi-smooth kernels. These equations, characterised by ill-posedness and sensitivity to input perturbations, are discretised using a composite closed Newton-Cotes quadrature scheme. The study evaluates the computational performance and accuracy of the standard GM method, also referred to as the Full-Sweep Geometric Mean (FSGM), in comparison with the Half-Sweep Geometric Mean (HSGM) and Quarter-Sweep Geometric Mean (QSGM) methods. Numerical experiments demonstrate significant reductions in computational complexity and execution time while maintaining high solution accuracy. The QSGM method achieves the best performance among the tested methods, highlighting its effectiveness in addressing computational challenges associated with first-kind Fredholm integral equations. Elsevier Ltd 2024-11 Article PeerReviewed pdf en cc_by_nc_4 http://umpir.ump.edu.my/id/eprint/43051/1/Numerical%20solution%20of%20first%20kind%20Fredholm%20integral%20equations%20with%20semi-smooth%20kernel.pdf Muthuvalu, Mohana Sundaram and Nor Aida Zuraimi, Md Noar and Harry, Setiawan and Isman, Kurniawan and Momani, Shaher (2024) Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach. Results in Applied Mathematics, 24 (100520). pp. 1-9. ISSN 2590-0374. (Published) https://doi.org/10.1016/j.rinam.2024.100520 https://doi.org/10.1016/j.rinam.2024.100520 |
| spellingShingle | QA Mathematics Muthuvalu, Mohana Sundaram Nor Aida Zuraimi, Md Noar Harry, Setiawan Isman, Kurniawan Momani, Shaher Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach |
| title | Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach |
| title_full | Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach |
| title_fullStr | Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach |
| title_full_unstemmed | Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach |
| title_short | Numerical solution of first kind Fredholm integral equations with semi-smooth kernel: A two-stage iterative approach |
| title_sort | numerical solution of first kind fredholm integral equations with semi-smooth kernel: a two-stage iterative approach |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/43051/ http://umpir.ump.edu.my/id/eprint/43051/ http://umpir.ump.edu.my/id/eprint/43051/ http://umpir.ump.edu.my/id/eprint/43051/1/Numerical%20solution%20of%20first%20kind%20Fredholm%20integral%20equations%20with%20semi-smooth%20kernel.pdf |