Volume No. :   6

Issue No. :  1

Year :  2015

ISSN Print :  0976-2973

ISSN Online :  2321-581X


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



Address:   Munish Kansal*, V. Kanwar and Saurabh Bhatia
University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India
DOI No: 10.5958/2321-581X.2015.00033.1

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.
KEYWORDS:
Nonlinear equations, Steffensen’s method, King’s method, Ostrowski’s method, Efiiciency index, Optimal order of convergence.
Cite:
Munish Kansal, V. Kanwar ,Saurabh Bhatia. On improved Steffensen type methods with optimal eighth-order of convergence. Research J. Engineering and Tech. 6(1): Jan.-Mar. 2015 page 223-228.
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