Modified King’s Family for Multiple Zeros of Scalar Nonlinear Functions

Ramandeep Behl, Munish Kansal and Mehdi Salimi
Additional contact information
Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Munish Kansal: School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, India
Mehdi Salimi: DiGiES & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy

Mathematics, 2020, vol. 8, issue 5, 1-17

Abstract: There is no doubt that there is plethora of optimal fourth-order iterative approaches available to estimate the simple zeros of nonlinear functions. We can extend these method/methods for multiple zeros but the main issue is to preserve the same convergence order. Therefore, numerous optimal and non-optimal modifications have been introduced in the literature to preserve the order of convergence. Such count of methods that can estimate the multiple zeros are limited in the scientific literature. With this point, a new optimal fourth-order scheme is presented for multiple zeros with known multiplicity. The proposed scheme is based on the weight function strategy involving functions in ratio. Moreover, the scheme is optimal as it satisfies the hypothesis of Kung–Traub conjecture. An exhaustive study of the convergence is shown to determine the fourth order of the methods under certain conditions. To demonstrate the validity and appropriateness for the proposed family, several numerical experiments have been performed. The numerical comparison highlights the effectiveness of scheme in terms of accuracy, stability, and CPU time.

Keywords: scalar nonlinear equations; multiple zeros; king’s family; optimal method; Kung–Traub conjecture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/5/827/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/5/827/ (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:8:y:2020:i:5:p:827-:d:360275

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 ().