Some Novel Newton-Type Methods for Solving Nonlinear Equations

被引：0

作者：

Bisheh-Niasar, Morteza ^{[1
]}

Saadatmandi, Abbas ^{[1
]}

机构：

[1] Univ Kashan, Dept Appl Math, Fac Math Sci, Kashan 8731753153, Iran

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2020年 / 38卷 / 03期

关键词：

Nonlinear equation; Newton's method; Order of convergence; Efficiency index; Iterative method; CUBIC CONVERGENCE;

D O I：

10.5269/bspm.v38i3.37351

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to present a new nonstandard Newton iterative method for solving nonlinear equations. The convergence of the proposed method is proved and it is shown that the new method has cubic convergence. Furthermore, two new multi-point methods with sixth-order convergence, based on the introduced method, are presented. Also, we describe the basins of attraction for these methods. Finally, some numerical examples are given to show the performance of our methods by comparing with some other methods available in the literature.

引用

页码：111 / 123

页数：13

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