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Affiliation of Author(s):数学与统计学院

Teaching and Research Group:数学教研室

Journal:Open Mathematics

Funded by:省、市、自治区科技项目

Key Words:iterative methods, Newton’s method, Cauchy’s method, order of convergence, Pade′ approximant

Abstract:In this paper, we derive and analyze a new one-parameter family of modied Cauchy method free from second derivative for obtaining simple roots of nonlinear equations by using Pade′ approximant. The convergence analysis of the family is also considered, and the methods have convergence order three. Based on the family of third-order method, in order to increase the order of the convergence, a new optimal fourth-order family of modied Cauchy methods is obtained by using weight function. We also perform some numerical tests and the comparison with existing optimal fourth-order methods to show the high computational eciency of the proposed scheme, which conrm our theoretical results. The basins of attraction of this optimal fourth-order family and existing fourth-order methods are presented and compared to illustrate some elements of the proposed family have equal or better stable behavior in many aspects. Furthermore, from the fractal graphics, with the increase of the value m of the series in iterative methods, the chaotic behaviors of the methods become more and more complex, which also reected in some existing fourth-order methods.

First Author:liutianbao

Indexed by:Journal paper

Volume:17

Issue:1

Page Number:1

Number of Words:4

ISSN No.:2391-5455

Translation or Not:no

Date of Publication:2019-12-31