Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 12 (2017), 51 -- 63

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This work is licensed under a Creative Commons Attribution 4.0 International License.

LOCAL CONVERGENCE OF SOME HIGH ORDER ITERATIVE METHODS BASED ON THE DECOMPOSITION TECHNIQUE USING ONLY THE FIRST DERIVATIVE

Ioannis K. Argyros and Santhosh George

Abstract. We present a local convergence analysis of some high order iterative methods based on the decomposition technique using only the first derivative for solving equations in order to approximate a solution of a nonlinear equation. In earlier studies hypotheses on the higher derivatives are used. Thus by using only first derivative, we extended the applicability of these methods. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

2010 Mathematics Subject Classification: 65D10; 65D99
Keywords: Ninth order method; efficiency index; local convergence; nonlinear equation.

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Ioannis K. Argyros
Department of Mathematical Sciences,
Cameron University,
Lawton, OK 73505, USA.
e-mail: iargyros@cameron.edu


Santhosh George
Department of Mathematical and Computational Sciences,
NIT Karnataka,
India-575 025.
e-mail:sgeorge@nitk.ac.in


http://www.utgjiu.ro/math/sma