Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs

S. D. Yakubu; P. Sibanda

doi:10.61298/rans.2025.3.2.142

Authors

S. D. Yakubu [email protected] Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, Nigeria School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa https://orcid.org/0000-0002-4721-2372
P. Sibanda School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa https://orcid.org/0000-0003-2115-4642

Keywords:

Fourth-derivative, Optimized hybrid block method, Stiff ODEs

Abstract

This paper introduces a single-step optimized fourth-derivative block hybrid method specifically designed to solve general third-order initial value problems directly. By incorporating advanced optimization techniques, the method significantly improves accuracy and computational efficiency. Extensive analysis confirms that the method exhibits zero-stability, consistency, A-stability, and convergence properties. Numerical experiments conducted in this study reveal that the proposed method surpasses existing approaches in accuracy, establishing it as a significant advancement in the numerical solution of higher-order initial value problems.

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