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On the Efficiency of a One-Fifth Step Hybrid Block Method for the Numerical Solution of Second-Order Ordinary Differential Equations Taiwo, Oluwasayo Esther
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 2 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i2.5497

Abstract

In this paper, hybrid methods for solving second-order ordinary differential equations with a one-fourth step length were developed. This was accomplished using interpolation and collocation techniques. The methods were evaluated based on the properties of linear multistep methods and were found to be zero-stable, consistent, and convergent, exhibiting a favorable region of absolute stability. The proposed methods were implemented for second-order ordinary differential initial value problems. The performance of the new methods demonstrated superiority over previously developed methods in the literature, as evidenced by the resolution of five numerical examples. The results were presented in tabular form.

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