Modification of Third-Order Iterative Method without Second Derivative for Solving Nonlinear Equation

Wartono ¹ , M. Soleh² , R. K. Pertiwi³

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.4 , pp.1-7, Aug-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.17

Online published on Aug 31, 2019

Copyright © Wartono, M. Soleh, R. K. Pertiwi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we propose a new two-point iterative method with two real parameters for solving nonlinear equation. We derive the method based on the linear combination of two third-order iterative methods. The proposed method still contains first and second derivative of f(x). To reduce the number of functional evaluations, the first and second derivative are approached by equality of two third-order iterative methods and parabolic equation, respectively. The convergence analysis shows that the proposed method has fourth-order convergence for  = ( 2)/(  0.5). The proposed method requires three evaluation of functions per iteration with efficiency index equal to 1.5874. Numerical simulation is presented to illustrate the comparison of efficiency and performance of the proposed method, Newton’s method, Chebyshev’s method and Homeier’s method by using several test functions. The result of numerical simulation shows that the performance of the proposed method better than other discussed methods.

Key-Words / Index Term :
Efficiency index, Chebyshev’s method, Homier’s method, order of convergence, nonlinear equation

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