NEWLY DEVELOPED SINGLE-STEP BLOCK METHOD FOR NUMERICAL SOLUTION OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

Year 2026, Volume: 16 Issue: 3, 397 - 408, 17.03.2026

Adebayo Femi Adebiyi Adaobi Mmachukwu Udoye Lukman Akinola , David Adeleke Mathew

https://izlik.org/JA98DR99YX

Abstract

This paper focuses on the development of a new block method for solving fourth order initial value problems of ordinary differential equations. Applying Chebyshev polynomial as a basis function, the method was developed using interpolation and collocation approaches. The convergence property of the method was established with zero-stability and consistency. Comparison was made with existing method, and the newly developed method compares favourably well.

Keywords

Numerical solution , Chebyshev polynomial , Error analysis , Zero stability , Convergence

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