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Research Journal of Engineering and Technology
ISSN: 2321-581X(Online), 0976-2973(Print)
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On improved Steffensen type methods with optimal eighth-order of convergence
Munish Kansal*, V. Kanwar and Saurabh Bhatia
University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India
This paper presents an improvement of the existing eighth-order derivative involved method  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.
Nonlinear equations, Steffensen’s method, King’s method, Ostrowski’s method, Efiiciency index, Optimal order of convergence.
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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