On dynamics of iterative techniques for nonlinear equation with applications in engineering
type: Item
instance of: scholarly article
title: On dynamics of iterative techniques for nonlinear equation with applications in engineering
zbMATH Open document ID: 1459.65061
DOI: 10.1155/2020/5853296
author: Mudassir Shams
author: Nazir Ahmad Mir
author: Naila Rafiq
author: A. Othman Almatroud
author: Saima Akram
published in: Mathematical Problems in Engineering
publication date: 2020-07-13T00:00:00Z
review text: Summary: In this article, we construct an optimal family of iterative methods for finding the single root and then extend this family for determining all the distinct as well as multiple roots of single-variable nonlinear equations simultaneously. Convergence analysis is presented for both the cases to show that the optimal order of convergence is 4 in the case of single root finding methods and 6 for simultaneous determination of all distinct as well as multiple roots of a nonlinear equation. The computational cost, basins of attraction, efficiency, log of residual, and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in the literature.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 7219949
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/5853296
OpenAlex ID: W3037366070
cites work: Construction of Newton-like iteration methods for solving nonlinear equations
cites work: Some variants of King's fourth-order family of methods for nonlinear equations
cites work: Some fourth-order iterative methods for solving nonlinear equations
cites work: New modifications of Potra-Pták's method with optimal fourth and eighth orders of convergence
cites work: A note on \(Q\)-order of convergence
cites work: A Family of Fourth Order Methods for Nonlinear Equations
cites work: A composite fourth-order iterative method for solving nonlinear equations
cites work: A fourth order iterative method for solving nonlinear equations
cites work: On Approximation of Equations by Algebraic Equations
cites work: Optimal Order of One-Point and Multipoint Iteration
cites work: Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation
cites work: Finding the roots of a polynomial on an MIMD multicomputer
cites work: On some methods for the simultaneous determination of polynomial zeros
cites work: Some families of two-step simultaneous methods for determining zeros of nonlinear equations
cites work: Iterative methods for simultaneous computing arbitrary number of multiple zeros of nonlinear equations
cites work: An improvement on two iteration methods for simultaneous determination of the zeros of a polynomial
cites work: On an efficient method for the simultaneous approximation of polynomial multiple roots
cites work: Semilocal convergence of Chebyshev-like root-finding method for simultaneous approximation of polynomial zeros
cites work: On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously
cites work: On the convergence of Halley's method for simultaneous computation of polynomial zeros
cites work: A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich's and Dochev-Byrnev's methods
cites work: General convergence theorems for iterative processes and applications to the Weierstrass root-finding method
cites work: On the local convergence of Ehrlich method for numerical computation of polynomial zeros
cites work: Convergence analysis of Sakurai-Torii-Sugiura iterative method for simultaneous approximation of polynomial zeros
cites work: Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
cites work: Generating root-finder iterative methods of second order: convergence and stability
cites work: Chaos in King's iterative family
cites work: Stability and applicability of iterative methods with memory
description: scientific article; zbMATH DE number 7219949