A new optimal family of three-step methods for efficient finding of a simple root of  a nonlinear equation

Nebojša M. Ralević; Dejan Ćebić

Vol. 21 No. 2 (2016)

Regular Articles

A new optimal family of three-step methods for efficient finding of a simple root of a nonlinear equation

Published 2016-02-22

Nebojša M. Ralević
Dejan Ćebić

Nebojša M. Ralević
Faculty of Engineering, University of Novi Sad

Dejan Ćebić
Faculty of Engineering, University of Novi Sad

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Abstract

This study presents a new efficient family of eighth order methods for finding the simple root of nonlinear equation. The new family consists of three steps: the Newton's step, any optimal fourth order iteration scheme and the simply structured third step which improves the convergence order up to at least eight, and ensures the efficiency index 1.6818. For several relevant numerical test functions, the numerical performances confirm the theoretical results.

Keywords

nonlinear equation, iterative methods, eighth-order convergence, optimal methods, divided differences

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