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Journal of Applied Mathematics and Computing

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21-10-2021 | Original Research

A new fifth-order iterative method free from second derivative for solving nonlinear equations

Authors: Noori Yasir Abdul-Hassan, Ali Hasan Ali, Choonkil Park

Published in: Journal of Applied Mathematics and Computing | Issue 5/2022

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Abstract

In this recent work, a new two-step iterative method for solving nonlinear equations that have a fifth-order convergence is suggested and analyzed. This new iterative method is free from second derivative of functions and based on Halley’s method and Taylor’s expansion together by using Hermite orthogonal polynomials basis to implement a suitable approximation of second derivative of functions. In addition, the order of convergence and the corresponding error equations of the new method are proved. Finally, some numerical examples are given to show the efficiency and the performance of the new method as well as a comparison with the original well-known Newton’s method and some other relevant methods are illustrated.

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Title: A new fifth-order iterative method free from second derivative for solving nonlinear equations
Authors: Noori Yasir Abdul-Hassan
Ali Hasan Ali
Choonkil Park
Publication date: 21-10-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 5/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01647-1

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