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 | ||
| Volume 17, Issue 2, December 2023, Pages 125-140 PDF (582.85 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2023.143686.1086 | ||
| Author | ||
| Saidu Daudu Yakubu* | ||
| School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Hybrid Optimized Third Derivative Method | ||
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