Convergence and Dynamics of a Higher-Order Method

Alejandro Moysi, Ioannis K. Argyros, Samundra Regmi, Daniel González, Á. Alberto Magreñán, Juan Antonio Sicilia
2020 Symmetry  
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
more » ... ts 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.
doi:10.3390/sym12030420 fatcat:no2redl5ofcy7e7xtapnswooqi