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

Year 2025, Volume: 22 Issue: 2, 90 - 101, 01.11.2025

Bello Kareem Akanbi , Oyedepo Taiye , Ayinde Muhammed Abdullahi , Raji Musiliu Tayo

https://izlik.org/JA59WA37HH

Abstract

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.

Keywords

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

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