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Abstract

The solution of differential equations, whether through analytical or numerical approaches, remains a fundamental problem in applied mathematics. Various numerical methods, including Euler’s method, the Runge-Kutta method, and Taylor series, have been widely used to solve first-order ordinary differential equations. Some researchers have explored these equations using Newton’s interpolation method, while others have combined Newton’s method with Lagrange’s interpolation technique. This study introduces a hybrid approach that integrates Newton’s interpolation method with Aitken’s method to solve Bernoulli differential equations. The efficiency and accuracy of this hybrid method are analyzed through a series of examples, demonstrating its effectiveness compared to conventional numerical techniques.

Keywords

Aitken Method First Order Differential Equations Hybrid Method Lagrange Interpolation Method Newton Interpolation Method Numerical Method

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Osmani, S. A. B. (1403). A Study on the Solution of Bernoulli Differential Equations Using a Hybrid Numerical Method. Journal of Natural Sciences – Kabul University, 7(4), 183–207. https://doi.org/10.62810/jns.v7i4.77
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