Hussaini HajaratMuhammad RaihanatuYusuf Abdulhakeem2025-04-292024http://repository.futminna.edu.ng:4000/handle/123456789/1188This research work presents the derivation and implementation of a 4-step linear multistep method of block hybrid backward differentiation formula for solving nonlinear second-order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the proposed numerical scheme where the legendary polynomial is adopted as a basic function. The 4-step BHBDF has higher order of accuracy p = 11 which implies that it is consistent. The proposed numerical block method is further applied to finding direct solution to nonlinear second order ordinary differentiation equations. This implementation strategy is more accurate than some existing methods considered in the literature.enlinear multi step methodblock methodhybridcollocation and interpolation methodsArticle