A Block Hybrid Method for the Direct Solution of y^(”)=f(x,y,y^(’)).

Ukoha Joseph Kalu; Mahmud Shamsuddeen Muhammed; Musa Idris Zainab; Zahid Ibrahim Shuaibu

doi:10.52589/AJMSS-BMGEEJXE

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A Block Hybrid Method for the Direct Solution of y^(”)=f(x,y,y^(’)).

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African Journal of Mathematics and Statistics Studies

Vol. 8Issue 12025pp. 220–234Published 8 April 2025

DOI 10.52589/AJMSS-BMGEEJXE

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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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Copyrights

Authors retain copyright in their articles and have unrestricted rights to reuse, republish, archive, share, and distribute their work after publication.
All articles are published open access under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence, which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, including for commercial purposes, provided appropriate credit is given to the original author(s) and source.