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Modelling and Simulation in Engineering
Volume 2015 (2015), Article ID 502854, 6 pages
http://dx.doi.org/10.1155/2015/502854
Research Article

A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order and Its Dynamics

Departamento de Ingenieria Civil, Facultad de Estudios Superiores (FES) Aragón, Universidad Nacional Autónoma de México (UNAM), Avenida Rancho Seco s/n, 57130 Nezahualcóyotl, MEX, Mexico

Received 30 September 2015; Accepted 24 November 2015

Academic Editor: Franco Ramírez

Copyright © 2015 Gustavo Fernández-Torres. 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.

Abstract

A geometric modification to the Newton-Secant method to obtain the root of a nonlinear equation is described and analyzed. With the same number of evaluations, the modified method converges faster than Newton’s method and the convergence order of the new method is . The numerical examples and the dynamical analysis show that the new method is robust and converges to the root in many cases where Newton’s method and other recently published methods fail.