Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs
This paper introduces three members of a one-step optimized third derivative hybrid block method family for solving general second-order initial value problems. The methodology incorporates optimization into the derivation process to achieve enhanced accuracy. Through rigorous analysis, it is demons...
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| Language: | English |
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Mosul University
2023-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_181639_3ca5d7513aca4b4326c58bb4835574a4.pdf |
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| _version_ | 1849768478006837248 |
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| author | Saidu Yakubu |
| author_facet | Saidu Yakubu |
| author_sort | Saidu Yakubu |
| collection | DOAJ |
| description | This paper introduces three members of a one-step optimized third derivative hybrid block method family for solving general second-order initial value problems. The methodology incorporates optimization into the derivation process to achieve enhanced accuracy. Through rigorous analysis, it is demonstrated that all the derived methods are found to be zero-stable, consistent, A-stable, and convergent. The implementation of these newly derived methods is validated through numerical experimentation, where the results exhibit superior accuracy compared to certain existing numerical methods explored in the study. All the newly derived optimized third derivative hybrid block methods possessed very small error constants with high order accuracy. |
| format | Article |
| id | doaj-art-7dd1e7e6fbd24765ae7d8bab4e45116a |
| institution | DOAJ |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-7dd1e7e6fbd24765ae7d8bab4e45116a2025-08-20T03:03:46ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902023-12-0117212514010.33899/csmj.2023.143686.1086181639Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPsSaidu Yakubu0School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South AfricaThis paper introduces three members of a one-step optimized third derivative hybrid block method family for solving general second-order initial value problems. The methodology incorporates optimization into the derivation process to achieve enhanced accuracy. Through rigorous analysis, it is demonstrated that all the derived methods are found to be zero-stable, consistent, A-stable, and convergent. The implementation of these newly derived methods is validated through numerical experimentation, where the results exhibit superior accuracy compared to certain existing numerical methods explored in the study. All the newly derived optimized third derivative hybrid block methods possessed very small error constants with high order accuracy.https://csmj.mosuljournals.com/article_181639_3ca5d7513aca4b4326c58bb4835574a4.pdfhybrid optimized third derivative method |
| spellingShingle | Saidu Yakubu Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs Al-Rafidain Journal of Computer Sciences and Mathematics hybrid optimized third derivative method |
| title | Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs |
| title_full | Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs |
| title_fullStr | Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs |
| title_full_unstemmed | Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs |
| title_short | Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs |
| title_sort | family of one step a stable optimized third derivative hybrid block methods for solving general second order ivps |
| topic | hybrid optimized third derivative method |
| url | https://csmj.mosuljournals.com/article_181639_3ca5d7513aca4b4326c58bb4835574a4.pdf |
| work_keys_str_mv | AT saiduyakubu familyofonestepastableoptimizedthirdderivativehybridblockmethodsforsolvinggeneralsecondorderivps |