Two new classes of optimal Jarratt-type fourth-order methods

In this paper, we investigate the construction of some two-step without memory iterative classes of methods for finding simple roots of nonlinear scalar equations. The classes are built through the approach of weight functions and these obtained classes reach the optimal order four using one functio...

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Bibliographic Details
Published inApplied mathematics letters Vol. 25; no. 5; pp. 847 - 853
Main Authors Soleymani, F., Khattri, S.K., Karimi Vanani, S.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2012
Subjects
Approximation
Derivatives
Efficiency index
Iterative methods
Jarratt-type methods
Kung–Traub conjecture
Mathematical analysis
Mathematical models
Multi-point iterations
Nonlinear equations
Optimal order
Optimization
Scalars
Kung–Traub conjecture
Jarratt-type methods
Optimal order
Efficiency index
Multi-point iterations
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Summary:In this paper, we investigate the construction of some two-step without memory iterative classes of methods for finding simple roots of nonlinear scalar equations. The classes are built through the approach of weight functions and these obtained classes reach the optimal order four using one function and two first derivative evaluations per full cycle. This shows that our classes can be considered as Jarratt-type schemes. The accuracy of the classes is tested on a number of numerical examples. And eventually, it is observed that our contributions take less number of iterations than the compared existing methods of the same type to find more accurate approximate solutions of the nonlinear equations.
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ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2011.10.030