A Modified Hybrid Method For Solving Non-Linear Equations With Computational Efficiency

This paper proposes a modified hybrid method for solving non-linear equations that improves computational efficiency while maintaining accuracy. The proposed method combines the advantages of the traditional Halley’s and mean-based methods, resulting in a more efficient algorithm. The modified hybrid method starts with Halley’s method and then switches to the mean-based method for rapid convergence. To further improve the efficiency of the algorithm, the proposed method incorporates a dynamic selection criterion to choose the appropriate method at each iteration. Numerical experiments are performed to evaluate the performance of the proposed method in comparison to other existing methods. The results show that the modified hybrid method is computationally efficient and can achieve high accuracy in a shorter time than other commonly used methods having similar features. The proposed method is applicable to a wide range of non-linear equations and can be used in various fields of science and engineering where non-linear equations arise. The modified hybrid method provides an effective tool for solving non-linear equations, offering significant improvements in computational efficiency over existing methods