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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| Main Authors: | , , |
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| Format: | Article |
| Language: | en |
| Published: |
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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| Summary: | 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. |
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