Second Derivative Free Eighteenth Order Convergent Method for Solving Non-Linear Equations

Author:

Kumar Vatti V.B.1,Sri Ramadevi2,Mylapalli M.S.Kumar2ORCID

Affiliation:

1. Dept. of Engineering Mathematics, Andhra University, Visakhapatnam, India.

2. Dept. of Mathematics, Gitam University, Visakhapatnam, India.

Abstract

In this paper, the Eighteenth Order Convergent Method (EOCM) developed by Vatti et.al is considered and this method is further studied without the presence of second derivative. It is shown that this method has same efficiency index as that of EOCM. Several numerical examples are given to illustrate the efficiency and performance of the new method. AMS Subject Classification: 41A25, 65K05, 65H05.

Publisher

Oriental Scientific Publishing Company

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference14 articles.

1. I.K. Argyros, S.K. Khattri, An improved semi local convergence analysis for the Chebyshev method.Journal of Applied Mathematics and computing.2013;42:1:(2):509-528, doi: 10.1007/s12190-013-0647-3.

2. M.A. Hafiz, Solving nonlinear equations using steffensen-type methods with optimal order of convergence. Palestine Journal of Mathematics.2014;3(1):113-119.

3. M.A. Hafiz, A new combined bracketing method for solving nonlinear equations. Journal of Mathematical and Computational Science.2013;3(1).

4. M.A. Hafiz, S.M.H. Al-Goria, Solving nonlinear equations using a new tenth-and seventh- order methods free from second derivative.International Journal of Differential Equations and Applications.2013;12(3):

5. 169-183,2013, doi: 10.12732/ijdea.v12i3.1344.

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