1. Convergence and Dynamics of a Higher-Order Method
- Author
-
Moysi, Alejandro, Argyros, Ioannis K., Regmi, Samundra, González, Daniel, Magreñán, A. Alberto, Sicilia, Juan Antonio, 0000-0002-7138-4385, 0000-0002-6991-5706, and 0000-0002-5962-4147
- Subjects
Physics ,Work (thermodynamics) ,Sequence ,convergence ,Physics and Astronomy (miscellaneous) ,Iterative method ,General Mathematics ,lcsh:Mathematics ,Contrast (statistics) ,010103 numerical & computational mathematics ,Derivative ,dynamics ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Chemistry (miscellaneous) ,Convergence (routing) ,Computer Science (miscellaneous) ,Order (group theory) ,Applied mathematics ,high-order iterative method ,0101 mathematics - 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.
- Published
- 2020