Comparative Analysis of Newton Midpoint Halley and Olver Methods for Solving the Roots of Nonlinear Equations
Abstract
Abstract: This study compares the Newton Midpoint Halley (NMH) method and the Olver Method in numerically solving the roots of non-linear equations. The main objective of this study is to evaluate the efficiency and convergence speed of both methods. Results show that the Newton Midpoint Halley method is superior in convergence, with a faster quadratic convergence rate and fewer iterations to achieve a certain accuracy than the Olver method. Although Olver's method is effective, NMH is able to achieve solutions with small errors in fewer iterations. In addition, the NMH method has a simpler and more intuitive algorithm, making it easier to implement in math teaching, especially for math education students. Although the Olver method offers higher accuracy, in terms of efficiency and ease of implementation, the Newton Midpoint Halley method is more recommended. Knowledge of both methods is important for students and can be applied in teaching and further applied mathematics research.
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