ON TWO-STEP PARALLEL COMPUTER ALGORITHM FOR ALL NONLINEAR EQUATIONS ROOTS WITH ENGINEERING APPLICATIONS

Mudassir Shams; Nasreen Kausar; Praveen Agarwal; Nouf Abdulrahman Alqahtani; Mdi Begum Jeelani

doi:10.1142/S0218348X26400141

ON TWO-STEP PARALLEL COMPUTER ALGORITHM FOR ALL NONLINEAR EQUATIONS ROOTS WITH ENGINEERING APPLICATIONS

Mudassir Shams
, Nasreen Kausar
, Praveen Agarwal
, Nouf Abdulrahman Alqahtani
, Mdi Begum Jeelani

Nonlinear Dynamic Research Centre (NDRC)

Balikesir University
Riphah International University
Yildiz Technical University
International College of Engineering
Al-Imam Muhammad Ibn Saud Islamic University

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

Abstract

In this paper, we develop an optimal family of two-step single root finding methods with order 4. Furthermore, we modify these numerical schemes to locate all nonlinear real and complex roots at the same time. The order of convergence is demonstrated using convergence analysis to be four for a single root-finding technique and for families of parallel computer methods. Numerical test examples reveal that the developed parallel techniques achieve superior stability and consistency compared to existing approaches.

Original language	English
Article number	2640014
Journal	Fractals
DOIs	https://doi.org/10.1142/S0218348X26400141
State	Accepted/In press - 2026

Keywords

Computational Time
Convergence
Fractal
Percentage Computational Cost
Polynomial
Simultaneous Methods

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10.1142/S0218348X26400141

Cite this

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title = "ON TWO-STEP PARALLEL COMPUTER ALGORITHM FOR ALL NONLINEAR EQUATIONS ROOTS WITH ENGINEERING APPLICATIONS",

abstract = "In this paper, we develop an optimal family of two-step single root finding methods with order 4. Furthermore, we modify these numerical schemes to locate all nonlinear real and complex roots at the same time. The order of convergence is demonstrated using convergence analysis to be four for a single root-finding technique and for families of parallel computer methods. Numerical test examples reveal that the developed parallel techniques achieve superior stability and consistency compared to existing approaches.",

keywords = "Computational Time, Convergence, Fractal, Percentage Computational Cost, Polynomial, Simultaneous Methods",

author = "Mudassir Shams and Nasreen Kausar and Praveen Agarwal and Alqahtani, \{Nouf Abdulrahman\} and Jeelani, \{Mdi Begum\}",

note = "Publisher Copyright: {\textcopyright} 2026 The Author(s)",

year = "2026",

doi = "10.1142/S0218348X26400141",

language = "English",

journal = "Fractals",

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T1 - ON TWO-STEP PARALLEL COMPUTER ALGORITHM FOR ALL NONLINEAR EQUATIONS ROOTS WITH ENGINEERING APPLICATIONS

AU - Shams, Mudassir

AU - Kausar, Nasreen

AU - Agarwal, Praveen

AU - Alqahtani, Nouf Abdulrahman

AU - Jeelani, Mdi Begum

PY - 2026

Y1 - 2026

N2 - In this paper, we develop an optimal family of two-step single root finding methods with order 4. Furthermore, we modify these numerical schemes to locate all nonlinear real and complex roots at the same time. The order of convergence is demonstrated using convergence analysis to be four for a single root-finding technique and for families of parallel computer methods. Numerical test examples reveal that the developed parallel techniques achieve superior stability and consistency compared to existing approaches.

AB - In this paper, we develop an optimal family of two-step single root finding methods with order 4. Furthermore, we modify these numerical schemes to locate all nonlinear real and complex roots at the same time. The order of convergence is demonstrated using convergence analysis to be four for a single root-finding technique and for families of parallel computer methods. Numerical test examples reveal that the developed parallel techniques achieve superior stability and consistency compared to existing approaches.

KW - Computational Time

KW - Convergence

KW - Fractal

KW - Percentage Computational Cost

KW - Polynomial

KW - Simultaneous Methods

UR - https://www.scopus.com/pages/publications/105033389870

U2 - 10.1142/S0218348X26400141

DO - 10.1142/S0218348X26400141

M3 - Article

AN - SCOPUS:105033389870

SN - 0218-348X

JO - Fractals

JF - Fractals

M1 - 2640014

ER -

ON TWO-STEP PARALLEL COMPUTER ALGORITHM FOR ALL NONLINEAR EQUATIONS ROOTS WITH ENGINEERING APPLICATIONS

Abstract

Keywords

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