A family of Newton-Chebyshev type methods to find simple roots of nonlinear equations and their dynamics | Zendy

Carlos E. Cadenas R. | Zendy

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A family of Newton-Chebyshev type methods to find simple roots of nonlinear equations and their dynamics

Author(s) -

Carlos E. Cadenas R.

Publication year - 2017

Publication title -

communications in numerical analysis

Language(s) - English

Resource type - Journals

ISSN - 2193-4215

DOI - 10.5899/2017/cna-00323

Subject(s) - simple (philosophy) , nonlinear system , mathematics , type (biology) , dynamics (music) , chebyshev filter , newton's method , mathematical analysis , calculus (dental) , physics , epistemology , ecology , philosophy , quantum mechanics , acoustics , biology , medicine , dentistry

In this work, a new family of Newton-Chebyshev type methods for solving nonlinear equations is presented. The dynamics of the Newton-Chebyshev family for the class of quadratic polynomials is analyzed and the convergence is established. We find the fixed and critical points. The stable and unstable behaviors are studied. The parameter space associated with the family is studied and finally, some dynamical planes that show different aspects of the dynamics of this family are presented

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