Two new efficient sixth order iterative methods for solving nonlinear equations

Obadah Said Solaiman; Ishak Hashim

doi:10.1016/j.jksus.2018.03.021

Two new efficient sixth order iterative methods for solving nonlinear equations

Obadah Said Solaiman
, Ishak Hashim

King Faisal University
Universiti Kebangsaan Malaysia

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

In this paper, we present two new iterative methods, one of them is second derivative free, for solving nonlinear equations. We derive these methods based on the Taylor series expansion and Halley's method. The convergence analysis of the two methods is discussed. It is established that the new methods have sixth order of convergence. Several numerical examples given show that the new methods are comparable with the well-known existing methods of the same order.

Original language	English
Pages (from-to)	701-705
Number of pages	5
Journal	Journal of King Saud University - Science
Volume	31
Issue number	4
DOIs	https://doi.org/10.1016/j.jksus.2018.03.021
State	Published - Oct 2019
Externally published	Yes

Keywords

Halley's method
Iterative methods
Nonlinear equations
Order of convergence
Root finding method

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10.1016/j.jksus.2018.03.021

Cite this

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abstract = "In this paper, we present two new iterative methods, one of them is second derivative free, for solving nonlinear equations. We derive these methods based on the Taylor series expansion and Halley's method. The convergence analysis of the two methods is discussed. It is established that the new methods have sixth order of convergence. Several numerical examples given show that the new methods are comparable with the well-known existing methods of the same order.",

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AU - Hashim, Ishak

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N2 - In this paper, we present two new iterative methods, one of them is second derivative free, for solving nonlinear equations. We derive these methods based on the Taylor series expansion and Halley's method. The convergence analysis of the two methods is discussed. It is established that the new methods have sixth order of convergence. Several numerical examples given show that the new methods are comparable with the well-known existing methods of the same order.

AB - In this paper, we present two new iterative methods, one of them is second derivative free, for solving nonlinear equations. We derive these methods based on the Taylor series expansion and Halley's method. The convergence analysis of the two methods is discussed. It is established that the new methods have sixth order of convergence. Several numerical examples given show that the new methods are comparable with the well-known existing methods of the same order.

KW - Halley's method

KW - Iterative methods

KW - Nonlinear equations

KW - Order of convergence

KW - Root finding method

UR - https://www.scopus.com/pages/publications/85044540213

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M3 - Article

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JO - Journal of King Saud University - Science

JF - Journal of King Saud University - Science

IS - 4

ER -

Two new efficient sixth order iterative methods for solving nonlinear equations

Abstract

Keywords

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