A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics. (9th December 2015)

• Record Type: Journal Article
• Authors: Fernández-Torres, Gustavo
• Other Names: Ramírez Franco Academic Editor.
• Is Part Of: Modelling and simulation in engineering. Volume 2015(2015)
• Publication Date: 2015-12-09
• Subjects: Engineering -- Simulation methods -- Periodicals; Engineering -- Mathematical models -- Periodicals; 620.004
• DOI: 10.1155/2015/502854
• Languages: English
• ISSNs: 1687-5591

Abstract

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 is1 + 2 ≈ 2.4142 . 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.