Research Journal of Engineering and Technology

Munish Kansal ¹, V. Kanwar ¹, Saurabh Bhatia ¹

Affiliations
1 University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, IN

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 derivativefree, 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.

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