An extended radius of convergence comparison between two sixth order methods under general continuity for solving equations

Open Access

Original research article

Author(s):

Samundra Regmi^a, Ioannis K. Argyros^b, Santhosh George^c, Christopher I. Argyros^d

^a Learning Commons, University of North Texas at Dallas, Dallas, TX, USA.
^b Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
^c Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka, India-575025.
^d Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA.

Advances in the Theory of Nonlinear Analysis and its Applications 6(3), 310-317.

Received: January 12, 2022

Accepted: March 13, 2022

Published: March 16, 2022

Abstract

In this paper, we compare the radius of convergence of two sixth-order convergence methods for solving nonlinear equations. We present the local convergence analysis not given before, which is based on the first Fréchet derivative that only appears in the method. Numerical examples where the theoretical results are tested complete the paper.

Keywords: Newton/Chebyshev method, Banach space, Local/semi-local convergence.

Share & Cite

APA Style

Regmi, S., Argyros, I. K., George, S., & Argyros, C. (2022). An extended radius of convergence comparison between two sixth order methods under general continuity for solving equations. Advances in the Theory of Nonlinear Analysis and its Application, 6(3), 310-317.