An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

Ramandeep Behl, Sonia Bhalla, Ángel Alberto Magreñán and Alejandro Moysi
Additional contact information
Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Sonia Bhalla: Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, Punjab, India
Ángel Alberto Magreñán: Department of Mathematics and Mathematics, University of La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
Alejandro Moysi: Department of Mathematics and Mathematics, University of La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain

Mathematics, 2021, vol. 9, issue 5, 1-19

Abstract: In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter ? to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

Keywords: nonlinear equations; Kung–Traub conjecture; multiple roots; optimal iterative methods; efficiency index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/5/546/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/5/546/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:5:p:546-:d:510892

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().