On the Efficiency of a One-Fifth Step Hybrid Block Method for the Numerical Solution of Second-Order Ordinary Differential Equations

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.