Hybrid continuous multi-step method for second order problems in ordinary differential equations

Oluwasayo Esther Taiwo; Nicholas S. Yakusak; Muideen O. Ogunniran

doi:10.26650/ijmath.2025.00021

Hybrid continuous multi-step method for second order problems in ordinary differential equations

Abstract

This study presents the development and analysis of a class of hybrid continuous methods designed for solving second-order initial value problems in ordinary differential equations. The formulation of the method is based on the application of a class of orthogonal and Chebyshev polynomials, which serve as a basis for the numerical approximation. The constructed scheme is subjected toarigorousstabilityandconvergenceanalysis,demonstratingitsreliabilityandsuitabilityfortheclassofproblemsunder consideration. To evaluate the method’s effectiveness, numerical experiments were conducted on selected benchmark problems from the literature. The results highlight the efficiency and accuracy of the proposed approach, showing improved numerical performance compared to existing methods. The hybrid continuous formulation ensures better approximation properties while maintaining computational efficiency. The stability properties confirm that the method remains robust across a range of problem scenarios, making it a viable tool for solving second-order differential equations. The study contributes to the ongoing advancement of numerical techniques for differential equations, particularly by leveraging hybrid continuous methods with polynomial-based approximations. The promising results from numerical experiments further establish the potential of this approach for broader applications in computational mathematics and applied sciences.

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Oluwasayo Esther Taiwo ^* This is me
0009-0002-2984-1375
Nigeria

Nicholas S. Yakusak This is me
0009-0009-5576-3463
Nigeria

Muideen O. Ogunniran This is me
0000-0003-4510-1254
Nigeria

Publication Date

June 24, 2025

Submission Date

October 15, 2024

Acceptance Date

April 4, 2025

Published in Issue

Year 2025 Volume: 3 Number: 1

DOI

https://doi.org/10.26650/ijmath.2025.00021

IZ

https://izlik.org/JA37KM57WG

Cite

RIS / Bibtex

APA

Taiwo, O. E., Yakusak, N. S., & Ogunniran, M. O. (2025). Hybrid continuous multi-step method for second order problems in ordinary differential equations. Istanbul Journal of Mathematics, 3(1), 1-11. https://doi.org/10.26650/ijmath.2025.00021

AMA

1.Taiwo OE, Yakusak NS, Ogunniran MO. Hybrid continuous multi-step method for second order problems in ordinary differential equations. Istanbul Journal of Mathematics. 2025;3(1):1-11. doi:10.26650/ijmath.2025.00021

Chicago

Taiwo, Oluwasayo Esther, Nicholas S. Yakusak, and Muideen O. Ogunniran. 2025. “Hybrid Continuous Multi-Step Method for Second Order Problems in Ordinary Differential Equations”. Istanbul Journal of Mathematics 3 (1): 1-11. https://doi.org/10.26650/ijmath.2025.00021.

EndNote

Taiwo OE, Yakusak NS, Ogunniran MO (June 1, 2025) Hybrid continuous multi-step method for second order problems in ordinary differential equations. Istanbul Journal of Mathematics 3 1 1–11.

IEEE

[1]O. E. Taiwo, N. S. Yakusak, and M. O. Ogunniran, “Hybrid continuous multi-step method for second order problems in ordinary differential equations”, Istanbul Journal of Mathematics, vol. 3, no. 1, pp. 1–11, June 2025, doi: 10.26650/ijmath.2025.00021.

ISNAD

Taiwo, Oluwasayo Esther - Yakusak, Nicholas S. - Ogunniran, Muideen O. “Hybrid Continuous Multi-Step Method for Second Order Problems in Ordinary Differential Equations”. Istanbul Journal of Mathematics 3/1 (June 1, 2025): 1-11. https://doi.org/10.26650/ijmath.2025.00021.

JAMA

1.Taiwo OE, Yakusak NS, Ogunniran MO. Hybrid continuous multi-step method for second order problems in ordinary differential equations. Istanbul Journal of Mathematics. 2025;3:1–11.

MLA

Taiwo, Oluwasayo Esther, et al. “Hybrid Continuous Multi-Step Method for Second Order Problems in Ordinary Differential Equations”. Istanbul Journal of Mathematics, vol. 3, no. 1, June 2025, pp. 1-11, doi:10.26650/ijmath.2025.00021.

Vancouver

1.Oluwasayo Esther Taiwo, Nicholas S. Yakusak, Muideen O. Ogunniran. Hybrid continuous multi-step method for second order problems in ordinary differential equations. Istanbul Journal of Mathematics. 2025 Jun. 1;3(1):1-11. doi:10.26650/ijmath.2025.00021