On Tenth‐Order Hybrid Numerov‐Type Methods

• DOI: 10.1002/mma.10835
• Publication Date: 2025-03-26T14:55:54Z
• Authors: Rabeh Abbassi; Sondess Ben Aoun; Mourad Kchaou; Theodore E. Simos; Charalampos Tsito...; Houssem Jerbi

ABSTRACTIn this paper, we introduce a new family of tenth‐order hybrid Numerov‐type methods designed for solving second‐order initial value problems (IVPs) with enhanced accuracy and efficiency. Our proposed methods build on the foundation of existing high‐order Numerov‐type techniques and incorporate advanced strategies for step size adaptation and error control. We provide a comprehensive analysis of the theoretical underpinnings of these methods and validate their performance through extensive numerical experiments.