# Two-Step Hybrid Block Method for Solving Second Order Initial Value Problem of Ordinary Differential Equations

• AbdulAzeez K. Jimoh Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Kwara State University, Malete, Nigeria
Keywords: linear multistep method, block method, hybrid points, zero-stability, consistency, convergence

### Abstract

A new zero-stable two-step hybrid block method for solving second order initial value problems of ordinary differential equations directly is derived and proposed. In the derivation of the method, the assumed power series solution is interpolated at the initial and the hybrid points while its second ordered derivative is collocated at all the nodal and selected off-step points in the interval of consideration. The relevant properties of the method were examined and the method was found to be zero-stable, consistent and convergent. A comparison of the results by the method with the exact solutions and other results in literature shows that the method is accurate, simple and effective in solving the class of problems considered.

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Published
2024-07-04
How to Cite
Jimoh, A. K. (2024). Two-Step Hybrid Block Method for Solving Second Order Initial Value Problem of Ordinary Differential Equations. Earthline Journal of Mathematical Sciences, 14(5), 1047-1065. https://doi.org/10.34198/ejms.14524.10471065
Section
Articles