Advertisement

Multidimensional Real Dynamics for High-Order Processes

  • Alicia CorderoEmail author
  • Javier G. Maimó
  • Juan R. Torregrosa
  • Maria P. Vassileva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

In this manuscript, we design a parametric family of iterative methods for solving nonlinear problems, that does not need to evaluate Jacobian matrices and needs to solve three linear systems per iteration with the same divided difference operator as coefficient matrix. The stability performance of the class is analyzed on a quadratic polynomial system and it is shown that for a wide set of values (including positive ones), there exist only convergence to the roots of the problem.

Keywords

Nonlinear systems Real multidimensional dynamics Stability 

Notes

Acknowledgement

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

References

  1. 1.
    Cordero, A., Gutiérrez, J.M., Magrenán, Á.A., Torregrosa, J.R.: Stability analysis of a parametric family of iterative methods for solving nonlinear models. Appl. Math. Comput. 285, 26–40 (2016)MathSciNetGoogle Scholar
  2. 2.
    Cordero, A., Soleymani, F., Torregrosa, J.R.: Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension? Appl. Math. Comput. 244, 398–412 (2014)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Robinson, R.C.: An Introduction to Dynamical Systems, Continous and Discrete. Americal Mathematical Society, Providence (2012)Google Scholar
  4. 4.
    Chicharro, F.I., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameters planes of iterative families and methods. Sci. World J. 2013, 11 (2013). Article ID 780153Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValènciaSpain
  2. 2.Instituto Tecnológico de Santo DomingoSanto DomingoDominican Republic

Personalised recommendations