Skip to main content
SpringerLink
Log in

Efficiency and Stability of a Family of Iterative Schemes for Solving Nonlinear Equations

  • 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:

  • 1292 Accesses

Abstract

In this paper, we construct a family of iterative methods with memory from one without memory, analyzing their convergence and stability. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Some numerical tests confirm the theoretical results.

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. (eds.): Advances in Iterative Methods for Nonlinear Equations. SSSS, vol. 10. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39228-8

    Book  MATH  Google Scholar 

  2. Amat, S., Busquier, S., Plaza, S.: Chaotic dynamics of a third-order Newton-type method. Math. Anal. Appl. 366(1), 24–32 (2010)

    Article  MathSciNet  Google Scholar 

  3. Arroyo, V., Cordero, A., Torregrosa, J.R.: Approximation of artificial satellites preliminary orbits: the efficiency challenge. Math. Comput. Model. 54, 1802–1807 (2011)

    Article  Google Scholar 

  4. Campos, B., Cordero, A., Torregrosa, J.R., Vindel, P.: A multidimensional dynamical approach to iterative methods with memory. Appl. Math. Comput. 271, 701–715 (2015)

    MathSciNet  Google Scholar 

  5. Campos, B., Cordero, A., Torregrosa, J.R., Vindel, P.: Stability of King’s family of iterative methods with memory. Comput. Appl. Math. 318, 504–514 (2017)

    Article  MathSciNet  Google Scholar 

  6. Magreñán, Á.A., Cordero, A., Gutiérrez, J.M., Torregrosa, J.R.: Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane. Math. Comput. Simul. 105, 49–61 (2014)

    Article  MathSciNet  Google Scholar 

  7. Petković, M.S., Neta, B., Petković, L.D., Džunić, J.: Multipoint Methods for Solving Nonlinear Equations. Elsevier, Amsterdam (2013)

    MATH  Google Scholar 

  8. Robinson, R.C.: An Introduction to Dynamical Systems: Continuous and Discrete. American Mathematical Society, Providence (2012)

    MATH  Google Scholar 

Download references

Acknowledgements

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 Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022, València, Spain

    Alicia Cordero & Juan R. Torregrosa

  2. Facultat de Matemàtiques, Universitat de València, València, Spain

    Ivan Giménez

Authors
  1. Alicia Cordero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivan Giménez
    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 Juan R. Torregrosa .

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., Giménez, I., Torregrosa, J.R. (2019). Efficiency and Stability of a Family of Iterative Schemes for Solving Nonlinear Equations. 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_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-11539-5_19

  • 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