A novel one-step optimized hybrid block method for solving general second-order ordinary differential equations
This study introduces a novel one-step hybrid block method for solving both stiff and non-stiff second-order ordinary differential equations (ODEs). The method incorporates optimization techniques and higher derivative functions, addressing the computational challenges of stiff ODEs while ensuring...
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| Format: | Article |
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FLAYOO PUBLISHING HOUSE LIMITED
2025-04-01
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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/135 |
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| author | Saidu Daudu Yakubu Precious Sibanda |
| author_facet | Saidu Daudu Yakubu Precious Sibanda |
| author_sort | Saidu Daudu Yakubu |
| collection | DOAJ |
| description |
This study introduces a novel one-step hybrid block method for solving both stiff and non-stiff second-order ordinary differential equations (ODEs). The method incorporates optimization techniques and higher derivative functions, addressing the computational challenges of stiff ODEs while ensuring key numerical properties such as zero-stability, A-stability, and convergence. Numerical experiments demonstrate the method’s effectiveness across various problems, including classical examples from heat conduction, electrical circuits, and the Van der Pol oscillator. The results reveal that the proposed method achieves superior accuracy and efficiency, significantly outperforming existing methods in the literature. These findings underscore the potential of this approach as a robust and versatile tool for solving a wide variety of practical ODEs in engineering and applied sciences.
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| format | Article |
| id | doaj-art-6150413ac3e44e2d9f435627eb0426e5 |
| institution | OA Journals |
| issn | 1596-0544 1596-0757 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | FLAYOO PUBLISHING HOUSE LIMITED |
| record_format | Article |
| series | Recent Advances in Natural Sciences |
| spelling | doaj-art-6150413ac3e44e2d9f435627eb0426e52025-08-20T02:25:42ZengFLAYOO PUBLISHING HOUSE LIMITEDRecent Advances in Natural Sciences1596-05441596-07572025-04-013110.61298/rans.2025.3.1.135A novel one-step optimized hybrid block method for solving general second-order ordinary differential equationsSaidu Daudu Yakubu0Precious Sibanda1https://orcid.org/0000-0003-2115-4642School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa, Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, NigeriaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa This study introduces a novel one-step hybrid block method for solving both stiff and non-stiff second-order ordinary differential equations (ODEs). The method incorporates optimization techniques and higher derivative functions, addressing the computational challenges of stiff ODEs while ensuring key numerical properties such as zero-stability, A-stability, and convergence. Numerical experiments demonstrate the method’s effectiveness across various problems, including classical examples from heat conduction, electrical circuits, and the Van der Pol oscillator. The results reveal that the proposed method achieves superior accuracy and efficiency, significantly outperforming existing methods in the literature. These findings underscore the potential of this approach as a robust and versatile tool for solving a wide variety of practical ODEs in engineering and applied sciences. https://flayoophl.com/journals/index.php/rans/article/view/135CollocationInterpolationFourth-derivative, Optimized hybrid block method, Stiff ODEsStiff ODEs |
| spellingShingle | Saidu Daudu Yakubu Precious Sibanda A novel one-step optimized hybrid block method for solving general second-order ordinary differential equations Recent Advances in Natural Sciences Collocation Interpolation Fourth-derivative, Optimized hybrid block method, Stiff ODEs Stiff ODEs |
| title | A novel one-step optimized hybrid block method for solving general second-order ordinary differential equations |
| title_full | A novel one-step optimized hybrid block method for solving general second-order ordinary differential equations |
| title_fullStr | A novel one-step optimized hybrid block method for solving general second-order ordinary differential equations |
| title_full_unstemmed | A novel one-step optimized hybrid block method for solving general second-order ordinary differential equations |
| title_short | A novel one-step optimized hybrid block method for solving general second-order ordinary differential equations |
| title_sort | novel one step optimized hybrid block method for solving general second order ordinary differential equations |
| topic | Collocation Interpolation Fourth-derivative, Optimized hybrid block method, Stiff ODEs Stiff ODEs |
| url | https://flayoophl.com/journals/index.php/rans/article/view/135 |
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