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

Authors

  • S. D. Yakubu
    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.

Dimensions

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Published

2025-07-30

How to Cite

Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs. (2025). Recent Advances in Natural Sciences, 3(2), 142. https://doi.org/10.61298/rans.2025.3.2.142

Issue

Volume 3, Issue 2, December 2025 (In Progress)

Section

Articles
Copyright & Licensing

Copyright (c) 2025 S. D. Yakubu, P. Sibanda

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs. (2025). Recent Advances in Natural Sciences, 3(2), 142. https://doi.org/10.61298/rans.2025.3.2.142