cujse

Cankaya University Journal of Science and Engineering

2564-7954

Cankaya University

Numerical Analysis

Sayısal Analiz

Robust Numerical Solutions of Higher-Order Stiff and Non-Stiff Third-Order Oscillatory Differential Equations Using a Direct Block Approach

https://orcid.org/0009-0007-6270-7705

Akanbi

Bello Kareem

University of Ilorin, Ilorin , Nigeria

https://orcid.org/0000-0001-9063-8806

Taiye

Oyedepo

Federal University of Allied Health Sciences Enugu

https://orcid.org/0000-0002-2563-0952

Abdullahi

Ayinde Muhammed

University of Abuja, Abuja

https://orcid.org/0000-0001-7466-393X

Tayo

Raji Musiliu

Federal University of Agriculture, Abeokuta

11 01 2025

22 2 90 101 08 06 2025 10 02 2025

2009

Cankaya University Journal of Science and Engineering

This work introduces a block algorithm formulated for directly solving third-order ordinary differential equations (ODEs), without the intermediate step of converting them into systems of first-order equations. The method is applied to three distinct types of problems non-stiff, oscillatory and stiff previously investigated by other researchers. Numerical results obtained using the proposed method are compared with those from existing methods in literature. The results reveal that the block algorithm consistently produces numerical solutions that closely align with the analytical solutions across all problem types. Graphical comparisons further demonstrate the superiority of the new method in terms of accuracy and stability. This confirms the method's effectiveness and versatility in solving higher-order ODEs directly, making it a valuable tool in computational mathematics.

Block Algorithm Third-order Differential Equations Direct Method Numerical Methods Numerical Solution Stiff ODEs Oscillatory Systems Non-stiff Problems

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