New Modification of Third-Order Iterative Method with Optimal Fourth-Order Convergence for Solving Nonlinear Equations

Wartono ¹ , Rahmawati ² , R. Agustin³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.155-161, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.155161

Online published on Feb 28, 2019

Copyright © Wartono, Rahmawati, R. Agustin . 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 :
Behl’s method is a third-order iterative method involving three functional evaluations for solving nonlinear equation. In this paper, we presented a new iterative method free second derivative with three real parameters by using second-order Taylor expansion. In order to avoid the second derivative, it is approximated by using equality of Chun-Kim’s method and Newton-Steffensen’s method. The result of study shows that the proposed method converges quartically and requires three evaluation of functions per iteration with efficiency index equal to 1.587401. Numerical simulation is presented to examine the performance of the proposed method by using several real test functions. The final results show that the proposed method is more efficient and perform better than some other kind of methods

Key-Words / Index Term :
Behl’s method, Chun-Kim’s method, Third-order iterative method, Newton-Steffensen’s method, Numerical simulation

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