Title: Hybridization of Bisection and Newton Methods for Solving Nonlinear Equations
Authors: Rana Hasan Hilal
Volume: 9
Issue: 4
Pages: 197-199
Publication Date: 2025/04/28
Abstract:
The hybridization of the Bisection and Newton methods for solving nonlinear equations offers a compelling approach to combine the strengths of both methods while mitigating their weaknesses. The Bisection method is known for its robustness and guaranteed convergence, especially when the initial guess is far from the actual root. However, it is slower compared to Newton's method, which converges rapidly but relies on a good initial guess and the computation of the derivative of the function. In this paper, we propose a hybrid method that starts with the Bisection method to ensure initial robustness and then switches to Newton's method to take advantage of its rapid convergence once the initial approximation is close enough to the root. The hybrid method is analyzed for its convergence properties and computational efficiency, and it is compared with both the Bisection and Newton methods through several numerical examples. Results show that the hybrid method offers a better balance between reliability and speed, making it a useful tool for solving nonlinear equations in practical applications where both accuracy and efficiency are important.