A Novel Seventh-Order Implicit Block Hybrid Nyström-Type Method for Second- Order Boundary Value Problems

Joel Olusegun Ajinuhi, Umaru Mohammed, Abdullah Idris Enagi and Jimoh Omananyi Razaq
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Joel Olusegun Ajinuhi: Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria
Umaru Mohammed: Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria
Abdullah Idris Enagi: Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria
Jimoh Omananyi Razaq: Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria

International Journal of Research and Scientific Innovation, 2023, vol. 10, issue 11, 26-44

Abstract: This 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.

Date: 2023
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