Order of Convergence, Extensions of Newton–Simpson Method for Solving Nonlinear Equations and Their Dynamics-Reference-Cited by-同舟云学术

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

Published:2023-02-06 Issue:2 Volume:7 Page:163
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

George Santhosh¹^ORCID,Kunnarath Ajil¹^ORCID,Sadananda Ramya¹^ORCID,Padikkal Jidesh¹^ORCID,Argyros Ioannis K.²^ORCID

Affiliation:

1. Department of Mathematical & Computational Science, National Institute of Technology Karnataka, Surathkal 575 025, India

2. Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Abstract

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.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/2/163/pdf

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