Journal of Prime Research in Mathematics

Construction of optimal derivative free iterative methods for nonlinear equations using Lagrange interpolation

Moin-ud-din Junjua
Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan.
Saima Akram\(^1\)
Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan.
Tariq Afzal
Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan.
Ayyaz Ali
Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan.
\(^{1}\)Corresponding Author: saimaakram@bzu.edu.pk
Copyright © 2020 Moin-ud-din Junjua, Saima Akram, Tariq Afzal, Ayyaz Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we present a general family of optimal derivative free iterative methods of arbitrary high order for solving nonlinear equations by using Lagrange interpolation. The special cases of this family with optimal order of convergence two, four, eight and sixteen are obtained. These methods do not need the Newton’s or Steffensen’s iterations in the first step of their iterative schemes. The advantage of the new schemes is that they are also extendable to the iterative methods with-memory. Numerical experiments and polynomiographs are presented to confirm the theoretical results and to compare the new iterative methods with other well known methods of similar kind.

Keywords:

Nonlinear equation, iterative methods, polynomiograph.