Skip to main content
SpringerLink
Log in

Stability of a Family of Iterative Methods of Fourth-Order

  • Conference paper
  • First Online:
Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

Included in the following conference series:

  • 1267 Accesses

Abstract

In this paper, we analyze the dynamical anomalies of a family of iterative methods, for solving nonlinear equations, designed by using weight function procedure. All the elements of the family are optimal schemes (in the sense of Kung-Traub conjecture) of fourth-order, but not all have the same stability properties. So, we describe the dynamical behavior of this family on quadratic polynomials. The study of fixed points and their stability, joint with the critical points and their associated parameter planes, show the richness of the presented class and allow us to select the members of the family with good stability properties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Amat, S., Busquier, S.: Advances in Iterative Methods foir Nonlinear Equations. SIMAI. Springer, Switzerland (2016)

    Book  Google Scholar 

  2. Blanchard, P.: The dynamics of Newton’s method. In: Proceedings of Symposium Applied Mathematics, vol. 49, pp. 139–154 (1994)

    Google Scholar 

  3. Blanchard, P.: Complex analytic dynamics on the Riemann sphere. Bull. AMS 11(1), 85–141 (1984)

    Article  MathSciNet  Google Scholar 

  4. Chicharro, F., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameter planes of iterative families and methods. Sci. World J. 2013 (2013). Article ID 780153

    Google Scholar 

  5. Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Math. 21, 634–651 (1974)

    Article  MathSciNet  Google Scholar 

  6. Petković, M., Neta, B., Petković, L.D., Džunić, J.: Multipoint Methods for Solving Nonlinear Equations. Academic Press, Amsterdam (2013)

    MATH  Google Scholar 

Download references

Acknowledgement

This research was partially supported by Ministerio de Economía y Competitividad under grants MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089.

Author information

Authors and Affiliations

  1. Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, València, Spain

    Alicia Cordero, Lucía Guasp & Juan R. Torregrosa

Authors
  1. Alicia Cordero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lucía Guasp
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juan R. Torregrosa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lucía Guasp .

Editor information

Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cordero, A., Guasp, L., Torregrosa, J.R. (2019). Stability of a Family of Iterative Methods of Fourth-Order. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-11539-5_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation