An Improved Blended Numerical Root-Solver for Nonlinear Equations

Abstract

This study presents a novel three-step iterative approach for solving nonlinear equations inthe domains of science and engineering. It represents a notable change from traditional methodslike Halley by eliminating the need for second derivatives. The suggested method exhibits asixth order of convergence and only requires five function evaluations, showcasing its efficiencywith an index of roughly 1.430969. The suggested method effectively solves nonlinear problemsinvolving equations with algebraic and transcendental terms. Comparative analysis againstexisting root-solving algorithms demonstrates their superior performance. The results not onlyconfirm the strength and effectiveness of the three-step iterative approach but also highlight itspotential for wide-ranging use in many scientific and technical situations.