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Author(s): Ukoha Joseph Kalu, Mahmud Shamsuddeen Muhammed, Musa Idris Zainab, Zahid Ibrahim Shuaibu.

Volume/Issue: Volume 8, Issue 1 (2025)

Page No: 220-234

Journal: African Journal of Mathematics and Statistics Studies (AJMSS)

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Abstract:

This paper introduces a Block Hybrid Method for solving general second-order ordinary differential equations (ODEs) with initial value problems. The method is based on a continuous formulation of the second-order hybrid generalized Adams method, incorporating one off-grid point per step. Discrete schemes are derived from the continuous form and its first derivative, forming the block methods. Analysis shows the method is consistent, zero-stable, and convergent. Numerical results highlight its superiority over existing methods.

Keywords:

Block Hybrid Method, Consistency, Zero-stability, Convergent, and Second Derivative.

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