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Research Journal of Engineering and Technology
Year : 2015, Volume : 6, Issue : 1
First page : ( 223) Last page : ( 228)
Print ISSN : 0976-2973. Online ISSN : 2321-581X.
Article DOI : 10.5958/2321-581X.2015.00033.1

On improved Steffensen type methods with optimal eighth-order of convergence

Kansal Munish*, Kanwar V.**, Bhatia Saurabh***

University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India

*E-mail: mkmaths23@pu.ac.in

**vmithil@yahoo.co.in

***s_bhatia@pu.ac.in

Mathematics Subject Classification (2000): 65H05, 65B99

Abstract

This paper presents an improvement of the existing eighth-order derivative involved method [14] into derivative-free scheme, holding the order of convergence of the original method. Each member of the family requires only four function evaluations per iteration to achieve the eighth-order of convergence, while they are totally free from derivative evaluation. Hence, they agree with the optimality conjecture of Kung-Traub for providing multipoint iterations without memory. The proposed methods are compared with their closest competitors in a series of numerical experiments. Numerical experiments show that such derivative-free, high order schemes offer significant advantages over the derivative involved methods.

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Keywords

Nonlinear equations, Steffensen's method, King's method, Ostrowski's method, Efiiciency index, Optimal order of convergence.

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