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- Title
Convergence and Dynamics of a Higher-Order Method.
- Authors
Moysi, Alejandro; Argyros, Ioannis K.; Regmi, Samundra; González, Daniel; Magreñán, Á. Alberto; Sicilia, Juan Antonio
- Abstract
Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method generating a sequence approximating the solution. That is why, in this work, we analyze the convergence in a local form for an iterative method with a high order to find the solution of a nonlinear equation. We extend the applicability of previous results using only the first derivative that actually appears in the method. This is in contrast to either works using a derivative higher than one, or ones not in this method. Moreover, we consider the dynamics of some members of the family in order to see the existing differences between them.
- Subjects
NONLINEAR equations; PROBLEM solving
- Publication
Symmetry (20738994), 2020, Vol 12, Issue 3, p420
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym12030420