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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...

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Main Authors: Muthuvalu, Mohana Sundaram, Nor Aida Zuraimi, Md Noar, Harry, Setiawan, Isman, Kurniawan, Momani, Shaher
Format: Article
Language:English
Published: Elsevier Ltd 2024
Subjects:
QA Mathematics
Online Access:http://umpir.ump.edu.my/id/eprint/43051/1/Numerical%20solution%20of%20first%20kind%20Fredholm%20integral%20equations%20with%20semi-smooth%20kernel.pdf
http://umpir.ump.edu.my/id/eprint/43051/
https://doi.org/10.1016/j.rinam.2024.100520
https://doi.org/10.1016/j.rinam.2024.100520
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spelling my.ump.umpir.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
institution Universiti Malaysia Pahang Al-Sultan Abdullah
building UMPSA Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang Al-Sultan Abdullah
content_source UMPSA Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
topic QA Mathematics
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
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.
format Article
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
title 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_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_sort numerical solution of first kind fredholm integral equations with semi-smooth kernel: a two-stage iterative approach
publisher Elsevier Ltd
publishDate 2024
url http://umpir.ump.edu.my/id/eprint/43051/1/Numerical%20solution%20of%20first%20kind%20Fredholm%20integral%20equations%20with%20semi-smooth%20kernel.pdf
http://umpir.ump.edu.my/id/eprint/43051/
https://doi.org/10.1016/j.rinam.2024.100520
https://doi.org/10.1016/j.rinam.2024.100520
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score 13.244413

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