Top

Published in:

2023 | OriginalPaper | Chapter

New Higher Order Iterative Method for Multiple Roots of Nonlinear Equations

Authors : Sunil Panday, Waikhom Henarita Chanu, Yumnam Nomita Devi

Published in: Frontiers in Industrial and Applied Mathematics

Publisher: Springer Nature Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The chapter introduces a new sixth-order iterative method for solving nonlinear equations with multiple roots, building upon Newton’s method. The development of this method is rigorously presented, including a proof of its sixth-order convergence. Numerical results are provided to compare the efficiency of the new method with existing sixth-order methods, showcasing its superior performance. The chapter concludes by highlighting the advantages of the new method, emphasizing its efficiency and simplicity in finding multiple roots of nonlinear equations.

AI Generated

This summary of the content was generated with the help of AI.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter A Computationally Efficient Sixth-Order Method for Nonlinear Models

next chapter Separation Axioms in Bipolar Fuzzy Topological Spaces

Traub, J.F.: Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, USA (1964)

Ostrowski, A.M.: Solution of Equations in Euclidean and Banach Space. Academic Press, New York, NY, USA (1973)

Jamaludin, N.A.A., Long, N.N., Salimi, M., Sharifi, S.: Review of some iterative methods for solving nonlinear equations with multiple zeros. Afrika Matematika 30(3–4), 355–369 (2019). https://doi.org/10.1007/s13370-018-00650-3

Thukral, R.: Introduction to higher-order iterative methods for finding multiple roots of nonlinear equations. Hindawi Publ. Corp. J. Math. (2013). https://doi.org/10.1155/2013/404635

Geum, Y.H., Kim, Y.I., Neta, B.: A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Appl. Math. Comput. 283, 120–140 (2016). https://doi.org/10.1016/j.amc.2016.02.029

Qudsi, R., Imran, M., Syamsudhuha: another six order iterative method free from derivatives for solving multiple roots of a nonlinear equation. Appl. Math. Sci. 43, 2121– 2129 (2017). https://doi.org/10.12988/ams.2017.76208

Singh, A., Jaiswal, J.P.: An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations. Proc. Natl. Acad. Sci. India, Sect. A Phys. Sci. 85, 439–450 (2015). https://doi.org/10.1007/s40010-015-0221-5

Behl, R., Al-Hamdan, W.M.: A 4th-order optimal extension of Ostrowski’s method for multiple zeros of univariate nonlinear functions. Math. MDPI 7(9) (2019). https://doi.org/10.3390/math7090803

Chanu, W.H., Panday, S., Dwivedi, M.: New fifth order iterative method for finding multiple root of nonlinear function. Eng. Lett.29(3) 942–947 (2021)

10.

Qudsi, R., Imran, M., Syamsudhuha: A sixth-order iterative method free from derivative for solving multiple roots of a nonlinear equation. Appl. Math. Sci. 8(2014), 5721–5730. https://doi.org/10.12988/ams.2014.47567

11.

Khattri, S.K.: How to increase convergence order of the newton method to 2m. Appl. Math. 59, 15–24 (2014). https://doi.org/10.1007/s10492-014-0038-6

Title: New Higher Order Iterative Method for Multiple Roots of Nonlinear Equations
Authors: Sunil Panday
Waikhom Henarita Chanu
Yumnam Nomita Devi
Publisher: Springer Nature Singapore
Book: Frontiers in Industrial and Applied Mathematics
Print ISBN: 978-981-19-7271-3

Electronic ISBN: 978-981-19-7272-0

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-981-19-7272-0_40

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"