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)
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Abstract
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.
| Item Type: | Article |
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| Uncontrolled Keywords: | First kind Fredholm integral equations; Semi-smooth kernel; Newton-cotes quadrature scheme; Dense linear system; Geometric Mean method; Complexity reduction approach |
| Subjects: | Q Science > QA Mathematics |
| Faculty/Division: | Center for Mathematical Science |
| Depositing User: | Mrs Norsaini Abdul Samat |
| Date Deposited: | 09 Dec 2024 01:34 |
| Last Modified: | 09 Dec 2024 01:34 |
| URI: | http://umpir.ump.edu.my/id/eprint/43051 |
| Download Statistic: | View Download Statistics |
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