Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations
1 Institute of Mathematics, National University of Mongolia, Mongolia
2 Joint Institute for Nuclear Research, Dubna, 141980 Moscow region, Russia
3 School of Applied Sciences, Mongolian University of Science and Technology, Mongolia
Published online: 14 February 2018
In this paper we propose a generating function method for constructing new two and three-point iterations with p (p = 4, 8) order of convergence. This approach allows us to derive a new family of optimal order iterative methods that include well known methods as special cases. Necessary and sufficient conditions for p-th (p = 4, 8) order convergence of the proposed iterations are given in terms of parameters τn and αn. We also propose some generating functions for τn and αn. We develop a unified representation of all optimal eighth-order methods. The order of convergence of the proposed methods is confirmed by numerical experiments.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).