Available online at www.worldscientificnews.com ( Received 31 December 2018; Accepted 15 January 2019; Date of Publication 16 January 2019 ) WSN 118 (2019) 236-250 EISSN 2392-2192 A Two-step Hybrid Block Method for the Numerical Integration of Higher Order Initial Value Problems of Ordinary Differential Equations Adoghe Lawrence Osa 1 and Omole Ezekiel Olaoluwa 2, * 1 Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State, Nigeria *2 Department of Mathematics & Statistics, Joseph Ayo Babalola University, Osun State, Nigeria *E-mail address: eoomole@jabu.edu.ng , omolez247@gmail.com ABSTRACT In this paper, a two-step implicit hybrid block multistep method is proposed for the approximate solution of higher order ordinary differential equations with a specification of fourth order. The study provides the use of both collocation and interpolation techniques to obtain the schemes. Direct form of power series is used as basis function for approximation solution. An order eight symmetric and zero- stable method is obtained. To implement our method, predictors of the same order of accuracy as the main method were developed using Taylor’s series algorithm. This implementation strategy is found to be efficient and more accurate as the result has shown in the numerical experiments. The result obtained confirmed the superiority of our method over existing methods Keywords: Hybrid, Block method, Fourth order, Collocation, Higher Order, power series, approximate solutions, zero stability, symmetry AMS Subject Classification: 65L02, 65L06, 65D30 1. INTRODUCTION In this paper, we considered the method of approximate solution of the general fourth order initial value problem of the form: