A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations
Integro-differential equations are critical for modelling real-world phenomena in physics, engineering, and biology. This paper introduces a Quadratic Mean iterative method to solve dense linear systems derived from the discretization of second and fourth-order Fredholm integro-differential equation...
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| Format: | Article |
| Language: | en |
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Penerbit Universiti Kebangsaan Malaysia
2025
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| Online Access: | http://journalarticle.ukm.my/26332/1/SMS%2016.pdf http://journalarticle.ukm.my/26332/ https://www.ukm.my/jsm/english_journals/vol54num9_2025/contentsVol54num9_2025.html |
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| author | Ng, Wei Li Elayaraja Aruchunan, Zailan Siri, |
| author_facet | Ng, Wei Li Elayaraja Aruchunan, Zailan Siri, |
| author_sort | Ng, Wei Li |
| building | Tun Sri Lanang Library |
| collection | Institutional Repository |
| content_provider | Universiti Kebangsaan Malaysia |
| content_source | UKM Journal Article Repository |
| continent | Asia |
| country | Malaysia |
| description | Integro-differential equations are critical for modelling real-world phenomena in physics, engineering, and biology. This paper introduces a Quadratic Mean iterative method to solve dense linear systems derived from the discretization of second and fourth-order Fredholm integro-differential equations (FIDEs). The solution of the FIDEs is approximated using finite difference, composite trapezoidal, and composite Simpson’s 1/3 and 3/8 schemes. The quadratic mean iterative method then solves the discretized system with different mesh sizes. As the resulting systems are large, a complexity reduction approach is implemented on the quadratic mean method to develop the half-sweep quadratic mean iterative method. The newly proposed iterative method includes a novel theorem, comprehensive proofs, and a detailed convergence analysis. The numerical results indicate that the quadratic mean method significantly outperforms the Gauss-Seidel iterative method in terms of efficiency, making it a promising solution for FIDEs. |
| format | Article |
| id | my-ukm.journal.26332 |
| institution | Universiti Kebangsaan Malaysia |
| language | en |
| publishDate | 2025 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| record_format | eprints |
| spelling | my-ukm.journal.263322026-01-05T08:26:41Z http://journalarticle.ukm.my/26332/ A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations Ng, Wei Li Elayaraja Aruchunan, Zailan Siri, Integro-differential equations are critical for modelling real-world phenomena in physics, engineering, and biology. This paper introduces a Quadratic Mean iterative method to solve dense linear systems derived from the discretization of second and fourth-order Fredholm integro-differential equations (FIDEs). The solution of the FIDEs is approximated using finite difference, composite trapezoidal, and composite Simpson’s 1/3 and 3/8 schemes. The quadratic mean iterative method then solves the discretized system with different mesh sizes. As the resulting systems are large, a complexity reduction approach is implemented on the quadratic mean method to develop the half-sweep quadratic mean iterative method. The newly proposed iterative method includes a novel theorem, comprehensive proofs, and a detailed convergence analysis. The numerical results indicate that the quadratic mean method significantly outperforms the Gauss-Seidel iterative method in terms of efficiency, making it a promising solution for FIDEs. Penerbit Universiti Kebangsaan Malaysia 2025 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/26332/1/SMS%2016.pdf Ng, Wei Li and Elayaraja Aruchunan, and Zailan Siri, (2025) A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations. Sains Malaysiana, 54 (9). pp. 2301-2313. ISSN 0126-6039 https://www.ukm.my/jsm/english_journals/vol54num9_2025/contentsVol54num9_2025.html |
| spellingShingle | Ng, Wei Li Elayaraja Aruchunan, Zailan Siri, A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations |
| title | A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations |
| title_full | A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations |
| title_fullStr | A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations |
| title_full_unstemmed | A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations |
| title_short | A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations |
| title_sort | novel variant of weighted quadratic mean iterative methods for fredholm integro-differential equations |
| url | http://journalarticle.ukm.my/26332/1/SMS%2016.pdf http://journalarticle.ukm.my/26332/ https://www.ukm.my/jsm/english_journals/vol54num9_2025/contentsVol54num9_2025.html |
| url_provider | http://journalarticle.ukm.my/ |