Using Majorizing Sequences for the Semi-local Convergence of a High-Order and Multipoint Iterative Method along with Stability Analysis

Authors

  • Mandana Moccari Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
  • Taher Lotfi Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

DOI:

https://doi.org/10.30495/jme.v0i0.1390

Keywords:

Majorizing sequence, High order of convergence, Semi-local convergence, Julia set, Basin of attraction

Abstract

This ‎paper‎ deals with the study of relaxed conditions for semi-local convergence for a general iterative method, k-step Newton's method, using ‎majorizing‎ sequences. Dynamical behavior of the mentioned method is also analyzed via Julia set and basins of attraction. Numerical examples of nonlinear systems of equations will be examined to clarify the given theory.

Author Biographies

Mandana Moccari, Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

Islamic Azad University of Hamedan

Taher Lotfi, Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

Islamic Azad University of Hamedan

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Published

2020-02-17

Issue

Vol. 15

Section

Vol. 15, No. 2, (2021)

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