On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously

Mudassir Shams; Naila Rafiq; Nasreen Kausar; Praveen Agarwal; Choonkil Park; Nazir Ahmad Mir

doi:10.1186/s13662-021-03616-1

On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously

Mudassir Shams
, Naila Rafiq
, Nasreen Kausar
, Praveen Agarwal
, Choonkil Park
, Nazir Ahmad Mir

Nonlinear Dynamic Research Centre (NDRC)

Riphah International University
National University of Modern Languages
Yildiz Technical University
International College of Engineering
Hanyang University

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

A highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous iterative method possesses 12th-order convergence locally. Numerical examples and computational cost are given to demonstrate the capability of the method presented.

Original language	English
Article number	465
Journal	Advances in Difference Equations
Volume	2021
Issue number	1
DOIs	https://doi.org/10.1186/s13662-021-03616-1
State	Published - Dec 2021

Keywords

CPU-time
Computational efficiency
Convergence order
Numerical scheme
Polynomials

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10.1186/s13662-021-03616-1

Cite this

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title = "On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously",

abstract = "A highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous iterative method possesses 12th-order convergence locally. Numerical examples and computational cost are given to demonstrate the capability of the method presented.",

keywords = "CPU-time, Computational efficiency, Convergence order, Numerical scheme, Polynomials",

author = "Mudassir Shams and Naila Rafiq and Nasreen Kausar and Praveen Agarwal and Choonkil Park and Mir, \{Nazir Ahmad\}",

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doi = "10.1186/s13662-021-03616-1",

language = "English",

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AU - Shams, Mudassir

AU - Rafiq, Naila

AU - Kausar, Nasreen

AU - Agarwal, Praveen

AU - Park, Choonkil

AU - Mir, Nazir Ahmad

PY - 2021/12

Y1 - 2021/12

N2 - A highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous iterative method possesses 12th-order convergence locally. Numerical examples and computational cost are given to demonstrate the capability of the method presented.

AB - A highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous iterative method possesses 12th-order convergence locally. Numerical examples and computational cost are given to demonstrate the capability of the method presented.

KW - CPU-time

KW - Computational efficiency

KW - Convergence order

KW - Numerical scheme

KW - Polynomials

UR - https://www.scopus.com/pages/publications/85117586824

U2 - 10.1186/s13662-021-03616-1

DO - 10.1186/s13662-021-03616-1

M3 - Article

AN - SCOPUS:85117586824

SN - 1687-1839

VL - 2021

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 465

ER -

On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously

Abstract

Keywords

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