Authors : Bako Jonathan Doyin; Timothy Freeman; Chep, Habila Magaji

Volume/Issue : Volume 9 - 2024, Issue 11 - November

Google Scholar : https://tinyurl.com/yehexnfc

Scribd : https://tinyurl.com/mt8brpda

DOI : https://doi.org/10.5281/zenodo.14293233

Abstract : This study introduces a new approach to the solution of second-order nonlinear differential equations, with a particular emphasis on the Bratu problems, which are highly relevant in many scientific domains. For this reason, the Block Hybrid Nystron-Type Method (BHNTM) was developed because the previous approaches to solve this problem had some drawbacks. Utilising the Bhaskera point obtained from the Bhaskeracosine approximation formula, BHNTM operates. By statistically searching for a power series polynomial, the method determines the coefficients in the most effective manner possible. The paper investigates BHNTM's convergence, zero stability, and consistency properties using numerical tests that indicate how accurate it is at solving Bratu-type issues. This study is a notable contribution to numerical analysis since it provides an alternative but successful technique to solving challenging second-order nonlinear differential equations, which is crucial in the scientific world.

Keywords : Hybrid Method; Blocknyström-Type Method; Nonlinear Odes; Power Series Polynomials; One- Dimensional Bratu Problems.

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