Family of One-Step A-Stable Optimized Third Derivative Hybrid Block Methods for Solving General Second-Order IVPs

• Published in: AL-Rafidain journal of computer sciences and mathematics Vol. 17; no. 2; pp. 125 - 140
• Main Author: Yakubu, Saidu
• Format: Journal Article
• Language: Arabic; English
• Published: Mosul University 23-12-2023
• Subjects: hybrid optimized third derivative method
• ISSN: 2311-7990; 1815-4816; 2311-7990
• DOI: 10.33899/csmj.2023.143686.1086

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.