Affiliation:
1. Faculty of Electronic Engineering, Department of Mathematics, Niš
2. Faculty of Mechanical Engineering, Niš
Abstract
An efficient family of two-point derivative free methods with memory for
solving nonlinear equations is presented. It is proved that the convergence
order of the proposed family is increased from 4 to at least 2 + ?6 ? 4.45,
5, 1/2 (5 + ?33) ? 5.37 and 6, depending on the accelerating technique. The
increase of convergence order is attained using a suitable accelerating
technique by varying a free parameter in each iteration. The improvement of
convergence rate is achieved without any additional function evaluations
meaning that the proposed methods with memory are very efficient. Moreover,
the presented methods are more efficient than all existing methods known in
literature in the class of two-point methods and three-point methods of
optimal order eight. Numerical examples and the comparison with the existing
two-point methods are included to confirm theoretical results and high
computational efficiency. 2010 Mathematics Subject Classification. 65H05
Publisher
National Library of Serbia
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
31 articles.
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