ABSRACT: In this article, an implicit one-step third derivative hybrid block method was developed for the numerical solution of first order initial value problems in ordinary differential Equations. In developing the method, interpolation and collocation techniques were considered for developing hybrid block methods. In developing the method we employed the conventional Taylor series expansion. To further justify the usability of the proposed method, the basic properties which infer convergence when adopted to solve ordinary differential equations were investigated. The proposed method validates its superiority over existing methods as seen in the accuracy of our results from the numerical examples. Furthermore, we called this formula OCB12 method

Keywords: Hybrid Block Method, First Order, Initial Value Problems, Taylor Series, Collocation, Interpolation, Third derivative.

| DOI: 10.17148/IARJSET.2021.8825