Order of Convergence, Extensions of Newton-Simpson Method for Solving Nonlinear Equations and Their Dynamics

被引：6

作者：

George, Santhosh ^{[1
]}

Kunnarath, Ajil ^{[1
]}

Sadananda, Ramya ^{[1
]}

Padikkal, Jidesh ^{[1
]}

Argyros, Ioannis K. ^{[2
]}

机构：

[1] Natl Inst Technol Karnataka, Dept Math & Computat Sci, Surathkal 575025, India

[2] Cameron Univ, Dept Comp & Math Sci, Lawton, OK 73505 USA

来源：

FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 02期

关键词：

order of convergence; Cordero-Torregrosa method; iterative method; Banach space; QUADRATURE-FORMULAS; ITERATIVE METHODS; SYSTEMS;

D O I：

10.3390/fractalfract7020163

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Local convergence of order three has been established for the Newton-Simpson method (NS), provided that derivatives up to order four exist. However, these derivatives may not exist and the NS can converge. For this reason, we recover the convergence order based only on the first two derivatives. Moreover, the semilocal convergence of NS and some of its extensions not given before is developed. Furthermore, the dynamics are explored for these methods with many illustrations. The study contains examples verifying the theoretical conditions.

引用

页数：22

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