An Improved Blended Numerical Root-Solver for Nonlinear Equations

Authors

DOI:

https://doi.org/10.21015/vtm.v12i1.1763

Abstract

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

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Published

2024-04-20

How to Cite

Asad Ali Chandio, Asif Ali Shaikh, Qureshi, S., & Abdul Rehman Soomroo. (2024). An Improved Blended Numerical Root-Solver for Nonlinear Equations. VFAST Transactions on Mathematics, 12(1), 164–175. https://doi.org/10.21015/vtm.v12i1.1763