Effectiveness of a One-fifth Hybrid Block Approach for Second Order Ordinary Differential Equations

Year 2023, Volume: 1 Issue: 2, 86 - 95, 17.12.2023

Oluwasayo Esther Taıwo Lateef Olakunle Moshood Muideen Odunayo Ogunnıran

Abstract

In this paper, a class of hybrid block methods for solving second order ordinary differential equations directly was developed. This class was obtained by interpolation and collocation techniques. The methods were analyzed based on the qualitative properties of linear multi-step methods and were found to be zero-stable, consistent and convergent with good region of absolute stability. The proposed methods were analyzed quantitatively and implemented on second order ordinary differential initial value problems. An improved performance of the new methods over existing methods in the literature was shown by solving five numerical examples. The results were presented in tabular form.

Keywords

Block method, hybrid method, initial value problems, one-fifth step, convergence, stability

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