A Class of Optimal Eighth-Order Steffensen-Type Iterative Methods for Solving Nonlinear Equations and their Basins of Attraction

Authors

Anuradha Singh, Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, M. P., 462003, IndiaFollow
J. P. Jaiswal, Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, M. P., 462003, IndiaFollow

Author Country (or Countries)

India

Abstract

This article concerned with the issue of solving a nonlinear equation with the help of iterative method where no derivative evaluation is required per iteration. Therefore, this work contributes to a new class of optimal eighth-order Steffensen-type methods. Theoretical proof has been given to reveal the eighth-order convergence. Numerical comparisons have been carried out to show the effectiveness of contributed scheme. Furthermore, we compare the performance of our proposed method by the basins of attraction with some existing eighth-order Steffensen-type methods.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100125

Recommended Citation

Singh, Anuradha and P. Jaiswal, J. (2016) "A Class of Optimal Eighth-Order Steffensen-Type Iterative Methods for Solving Nonlinear Equations and their Basins of Attraction," Applied Mathematics & Information Sciences: Vol. 10: Iss. 1, Article 25.
DOI: http://dx.doi.org/10.18576/amis/100125
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/25