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Using a carefully selected step and off-step points produced from the Bhaskara Cosine approximation formula and Gauss-Lobato grid points with constant step size, this numerical study presents the Block Hybrid Nyström-type method of order seven for solving the second order Bratu problem with impedance boundary conditions at two-point concurrently. Without the use of a combination of predictor-corrector mode and or the shooting approach, the solution is achieved immediately without having to convert it to a system of first order ordinary differential equations. The diffusion of heat produced by the application that imposed the impedance conditions is the focus of a numerically tested problem. The present findings showed that the proposed method produce an efficient performance in terms of accuracy, and error when compared with the existing methods. The convergence and stability properties of the BHNTM are discussed.



Bratu Problem; Hybrid (Bhaskara) points; Block Nyström-type method; Nonlinear ODEs; Power Series Polynomials, Bhaskara Cosine-Approximation formula; Impedance boundary conditions

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Theophilus, G. O., Olusegun, A. J., & Umaru, M. (2024). K-Step Block Hybrid Nyström-Type Method for the solution of Bratu problem with Impedance Boundary Condition. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 5(1), 34-46. Retrieved from


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