A new family of iterative methods based on an exponential model for solving nonlinear equations
type: Item
instance of: scholarly article
title: A new family of iterative methods based on an exponential model for solving nonlinear equations
zbMATH Open document ID: 1397.65072
DOI: 10.1155/2013/547438
author: Tianbao Liu
author: Hengyan Li
author: Zaixiang Pang
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: We present two new families of iterative methods for obtaining simple roots of nonlinear equations. The first family is developed by fitting the model \(m(x) = e^{px}(Ax^2 + Bx + C)\) to the function \(f(x)\) and its derivative \(f^{'}\), \(f^{''}\) at a point \(x_n\). In order to remove the second derivative of the first methods, we construct the second family of iterative methods by approximating the equation \(f(x)=0\) around the point \((x_n,f(x_n))\) by the quadratic equation. Analysis of convergence shows that the new methods have third-order or higher convergence. Numerical experiments show that new iterative methods are effective and comparable to those of the well-known existing methods.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6950743
Wikidata QID: Q59002974
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/547438
OpenAlex ID: W1966734271
description: scientific article; zbMATH DE number 6950743