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381185

Solving nonsmooth equations using family of derivative-free optimal methods

Article

Last updated: 31 Dec 2024

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Abstract

In this paper, a family of derivative-free of third and fourth order convergent methods
for solving nonlinear equations is suggested. In the proposed methods, several linear combinations
of divided differences are used in order to get a good estimation of the derivative of the given function
at the different steps of the iteration. The efficiency indices of the members of this family are
equal to 1.442 and 1.587. The convergence and error analysis are given. Numerical comparisons are
made with other existing methods to show the performance of the presented methods.

DOI

10.1016/j.joems.2012.10.007

Keywords

Nonlinear equations, Convergence analysis, Nonsmooth equations, Iterative methods, Derivative-free methods, Optimal order of convergence

Authors

First Name

M.A.

Last Name

Hafiz

MiddleName

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Affiliation

Department of Mathematics, Faculty of Science and Arts, Najran University, Najran 1988, Saudi Arabia

Email

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City

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Orcid

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First Name

Mohamed S.M.

Last Name

Bahgat

MiddleName

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Affiliation

Department of Mathematics, Faculty of Science, Minia University, Minia 61111, Egypt

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Orcid

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Volume

21

Article Issue

1

Related Issue

50461

Issue Date

2013-04-01

Receive Date

2024-09-23

Publish Date

2013-04-01

Page Start

38

Page End

43

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 21_Issue 1_Pages 38-43.pdf

PDF . 318.8kB

Link

https://joems.journals.ekb.eg/article_381185.html

Detail API

https://joems.journals.ekb.eg/service?article_code=381185

Order

381,185

Type

Original Article

Type Code

3,248

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

Solving nonsmooth equations using family of derivative-free optimal methods

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Type

Article

Created At

21 Dec 2024