Nusrat Yasmin, Saima Iftikhar
Centre for Advanced Studies in Pure and
Applied Mathematics
Bahauddin Zakariya University
Multan, PAKISTAN

Abstract. Some well-known methods involving first derivative create numerical difficulties and fail to converge in the neighborhood of the required root, so that in this paper, we have constructed two new sixth order and one seventh order convergence derivative free methods for solving nonlinear equations. The proposed methods are based on composition of Newton's method with known methods. Each derivative free method requires four functional evaluations per iteration. The new methods attain the efficiency indexes and respectively, which makes them competitive. Convergence analysis and numerical examples are also given to illustrate and compare the accuracy and efficiency of the proposed methods with existing methods.

Received: July 22, 2012

AMS Subject Classification: 65H04, 65H05

Key Words and Phrases: nonlinear equations, efficiency index, order of convergence, Steffensen like methods, computational order of convergence

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