**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

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