Joel Olusegun AjinuhiUmaru MohammedAbdullah Idris EnagiJIMOH, OMANANYI RAZAQ2025-04-162023-11-05https://doi.org/10.51244/IJRSI.2023.1011003http://repository.futminna.edu.ng:4000/handle/123456789/738This paper introduces a novel approach for solving second-order nonlinear differential equations, with a primary focus on the Bratu problem, which holds significant importance in diverse scientific areas. Existing methods for solving this problem have limitations, prompting the development of the Block Hybrid Nystrom-Type Method (BHNTM). BHNTM utilizes the Bhaskara points derived, using the Bhaskara cosine approximation formula. The method seeks a numerical solution in the form of a power series polynomial, efficiently determining coefficients. The paper discusses BHNTM's convergence, zero stability, and consistency properties, substantiated through numerical experiments, highlighting its accuracy as a solver for Bratu-type equations. This research contributes to the field of numerical analysis by offering an alternative, effective approach to tackle complex second-order nonlinear differential equations, addressing critical challenges in various scientific domains.enHybrid MethodBlockNyström-type methodNonlinear ODEsPower Series PolynomialsOne-dimensional Bratu problemsArticle