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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Main Author: Saidu Yakubu
Format: Article
Language:English
Published: Mosul University 2023-12-01
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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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
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institution DOAJ
issn 1815-4816
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publishDate 2023-12-01
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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