Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs
This paper introduces a single-step optimized fourth-derivative block hybrid method specifically designed to solve general third-order initial value problems directly. By incorporating advanced optimization techniques, the method significantly improves accuracy and computational efficiency. Extensi...
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| Format: | Article |
| Language: | English |
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FLAYOO PUBLISHING HOUSE LIMITED
2025-07-01
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| Series: | Recent Advances in Natural Sciences |
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| Online Access: | https://flayoophl.com/journals/index.php/rans/article/view/142 |
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| _version_ | 1849393827618488320 |
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| author | S. D. Yakubu P. Sibanda |
| author_facet | S. D. Yakubu P. Sibanda |
| author_sort | S. D. Yakubu |
| collection | DOAJ |
| description |
This paper introduces a single-step optimized fourth-derivative block hybrid method specifically designed to solve general third-order initial value problems directly. By incorporating advanced optimization techniques, the method significantly improves accuracy and computational efficiency. Extensive analysis confirms that the method exhibits zero-stability, consistency, A-stability, and convergence properties. Numerical experiments conducted in this study reveal that the proposed method surpasses existing approaches in accuracy, establishing it as a significant advancement in the numerical solution of higher-order initial value problems.
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| format | Article |
| id | doaj-art-37b79318062d4d1e8132b26a483b2de4 |
| institution | Kabale University |
| issn | 1596-0544 1596-0757 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | FLAYOO PUBLISHING HOUSE LIMITED |
| record_format | Article |
| series | Recent Advances in Natural Sciences |
| spelling | doaj-art-37b79318062d4d1e8132b26a483b2de42025-08-20T03:40:17ZengFLAYOO PUBLISHING HOUSE LIMITEDRecent Advances in Natural Sciences1596-05441596-07572025-07-013210.61298/rans.2025.3.2.142Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPsS. D. YakubuP. Sibanda This paper introduces a single-step optimized fourth-derivative block hybrid method specifically designed to solve general third-order initial value problems directly. By incorporating advanced optimization techniques, the method significantly improves accuracy and computational efficiency. Extensive analysis confirms that the method exhibits zero-stability, consistency, A-stability, and convergence properties. Numerical experiments conducted in this study reveal that the proposed method surpasses existing approaches in accuracy, establishing it as a significant advancement in the numerical solution of higher-order initial value problems. https://flayoophl.com/journals/index.php/rans/article/view/142Fourth-derivativeOptimized hybrid block methodStiff ODEs |
| spellingShingle | S. D. Yakubu P. Sibanda Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs Recent Advances in Natural Sciences Fourth-derivative Optimized hybrid block method Stiff ODEs |
| title | Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs |
| title_full | Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs |
| title_fullStr | Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs |
| title_full_unstemmed | Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs |
| title_short | Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs |
| title_sort | implicit one step optimized fourth derivative hybrid block method for directly solving general third order ivps |
| topic | Fourth-derivative Optimized hybrid block method Stiff ODEs |
| url | https://flayoophl.com/journals/index.php/rans/article/view/142 |
| work_keys_str_mv | AT sdyakubu implicitonestepoptimizedfourthderivativehybridblockmethodfordirectlysolvinggeneralthirdorderivps AT psibanda implicitonestepoptimizedfourthderivativehybridblockmethodfordirectlysolvinggeneralthirdorderivps |