IJPAM: Volume 83, No. 1 (2013)

FIFTH AND SIXTH-ORDER ITERATIVE ALGORITHMS
WITHOUT DERIVATIVES FOR SOLVING
NON-LINEAR EQUATIONS

G. Fernández-Torres$^1$, F.R. Castillo-Soria$^2$, I. Algredo-Badillo$^3$
$^1$Petroleum Engineering Department
Universidad del Istmo
Tehuantepec, Oaxaca, 70760, MÉXICO
$^2$Computer Engineering Department
Universidad del Istmo
Tehuantepec, Oaxaca, 70760, MÉXICO


Abstract. In this paper we will present two derivative free iterative methods for finding the root of a nonlinear equation $f(x) = 0$. The new methods are based on direct and inverse polynomial interpolation. We will prove that one of the methods has fifth-order convergence and the other method sixth-order convergence. Several examples will show that convergence and the efficiency of the new methods to be better than the classic Newton's method and others derivative free methods with high order of convergence previously presented.

Received: November 15, 2012

AMS Subject Classification: 65D05, 65D07, 65D15

Key Words and Phrases: nonlinear equations, iterative methods, roots finding method, derivative free, interpolation

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DOI: 10.12732/ijpam.v83i1.10 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 1