A single-step approach with seven hybrid points for the solution of stiff differential equations
This research presents a novel single-step hybrid block method with seven intra-step points that achieves ninth-order accuracy, providing an accurate and computationally efficient approach for solving first-order stiff differential equations. The method is designed to solve first-order stiff differe...
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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/26556/1/SMD%2012.pdf http://journalarticle.ukm.my/26556/ https://www.ukm.my/jsm/english_journals/vol54num12_2025/contentsVol54num12_2025.html |
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| _version_ | 1858061957975769088 |
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| author | Dibal, Ibrahim Mohammed Yeak, Su Hoe Suzarina Ahmed Sukri, |
| author_facet | Dibal, Ibrahim Mohammed Yeak, Su Hoe Suzarina Ahmed Sukri, |
| author_sort | Dibal, Ibrahim Mohammed |
| building | Tun Sri Lanang Library |
| collection | Institutional Repository |
| content_provider | Universiti Kebangsaan Malaysia |
| content_source | UKM Journal Article Repository |
| continent | Asia |
| country | Malaysia |
| description | This research presents a novel single-step hybrid block method with seven intra-step points that achieves ninth-order accuracy, providing an accurate and computationally efficient approach for solving first-order stiff differential equations. The method is designed to solve first-order stiff differential equations with high efficiency and precision while maintaining a constant step size throughout the computation. To further improve accuracy, Lagrange polynomial interpolation techniques are employed to approximate function values at selected points within each step. The fundamental properties of the proposed scheme are rigorously analysed to establish its mathematical validity. These analyses confirm that the method satisfies the essential conditions of consistency, stability, and convergence, thereby ensuring its reliability for applications. The proposed method performs effectively when applied to stiff and oscillatory differential equations. Comprehensive numerical experiments are conducted, and the results consistently demonstrate the robustness and effectiveness of the proposed method across various test problems. Furthermore, the findings indicate that the method often outperforms several existing numerical techniques in terms of both accuracy and computational efficiency. |
| format | Article |
| id | my-ukm.journal.26556 |
| institution | Universiti Kebangsaan Malaysia |
| language | en |
| publishDate | 2025 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| record_format | eprints |
| spelling | my-ukm.journal.265562026-02-11T05:02:05Z http://journalarticle.ukm.my/26556/ A single-step approach with seven hybrid points for the solution of stiff differential equations Dibal, Ibrahim Mohammed Yeak, Su Hoe Suzarina Ahmed Sukri, This research presents a novel single-step hybrid block method with seven intra-step points that achieves ninth-order accuracy, providing an accurate and computationally efficient approach for solving first-order stiff differential equations. The method is designed to solve first-order stiff differential equations with high efficiency and precision while maintaining a constant step size throughout the computation. To further improve accuracy, Lagrange polynomial interpolation techniques are employed to approximate function values at selected points within each step. The fundamental properties of the proposed scheme are rigorously analysed to establish its mathematical validity. These analyses confirm that the method satisfies the essential conditions of consistency, stability, and convergence, thereby ensuring its reliability for applications. The proposed method performs effectively when applied to stiff and oscillatory differential equations. Comprehensive numerical experiments are conducted, and the results consistently demonstrate the robustness and effectiveness of the proposed method across various test problems. Furthermore, the findings indicate that the method often outperforms several existing numerical techniques in terms of both accuracy and computational efficiency. Penerbit Universiti Kebangsaan Malaysia 2025 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/26556/1/SMD%2012.pdf Dibal, Ibrahim Mohammed and Yeak, Su Hoe and Suzarina Ahmed Sukri, (2025) A single-step approach with seven hybrid points for the solution of stiff differential equations. Sains Malaysiana, 54 (12). pp. 2937-2952. ISSN 0126-6039 https://www.ukm.my/jsm/english_journals/vol54num12_2025/contentsVol54num12_2025.html |
| spellingShingle | Dibal, Ibrahim Mohammed Yeak, Su Hoe Suzarina Ahmed Sukri, A single-step approach with seven hybrid points for the solution of stiff differential equations |
| title | A single-step approach with seven hybrid points for the solution of stiff differential equations |
| title_full | A single-step approach with seven hybrid points for the solution of stiff differential equations |
| title_fullStr | A single-step approach with seven hybrid points for the solution of stiff differential equations |
| title_full_unstemmed | A single-step approach with seven hybrid points for the solution of stiff differential equations |
| title_short | A single-step approach with seven hybrid points for the solution of stiff differential equations |
| title_sort | single-step approach with seven hybrid points for the solution of stiff differential equations |
| url | http://journalarticle.ukm.my/26556/1/SMD%2012.pdf http://journalarticle.ukm.my/26556/ https://www.ukm.my/jsm/english_journals/vol54num12_2025/contentsVol54num12_2025.html |
| url_provider | http://journalarticle.ukm.my/ |