Skip to content
Research Article Open access CC BY 4.0

Some New Three Step Iterative Methods for Solving Nonlinear Equation Using Steffensen’s and Halley Method

Najmuddin Ahmad, Vimal Pratap Singh

Journal of Advances in Mathematics and Computer Science · pp. 1–9 · Published 18 Oct 2016

10.9734/BJMCS/2016/29322

Abstract

In this paper, we introduce the comparative study of new three step iterative methods for finding the zeros of the nonlinear equation f(x) = 0. The new method based on the Steffensen’s method and Halley method with using predictor – corrector technique. It is established that the new method (NTSM-1) has convergence order sixth and second new method (NTSM-2) has convergence order seventh. Numerical tests show that the new methods is comparable with the well known existing methods and gives better results.

Non linear equations iterative methods three step convergence analysis Halley method Steffensen’s method

References (14)

  1. 1 Iterative Solution of Nonlinear Equations in Several Variables [DOI]
  2. 2 Solution of Equations and Systems of Equations [DOI]
  3. 3 The numerical treatment of a single nonlinear equation
  4. 4 Iterative methods improving newton's method by the decomposition method [DOI]
  5. 5 A new iterative method for solving nonlinear equations [DOI]
  6. 6 New family of iterative methods for nonlinear equations [DOI]
  7. 7 High order iterative methods without derivatives for solving nonlinear equations [DOI]
  8. 8 Algorithm for forming derivative-free optimal methods [DOI]
  9. 9 A Steffensen-like method and its higher-order variants [DOI]
  10. 10 Constructing third-order derivative-free iterative methods [DOI]
  11. 11 THREE-STEP ITERATIVE METHOD WITH EIGHTEENTH ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS [DOI]
  12. 12 Quadrature Based Optimal Iterative Methods with Applications in High-Precision Computing [DOI]
  13. 13 New two-step predictor-corrector method with ninth order convergence for solving nonlinear equations [DOI]
  14. 14 Numerical methods for scientific and engineering computation. [DOI]

Cited by 6

NOVEL APPROACH FOR EIGENVALUE PROBLEMS USING THE MONTE CARLO METHOD

FAUZIA SHAHEEN, NAJMUDDIN AHMAD · Journal of Science and Arts · 2023

An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots

Saima Akram, Fiza Zafar, Nusrat Yasmin · Mathematics · 2019

New three step derivative free iterative method for solving nonlinear equations

Najmuddin Ahmad, Vimal Pratap Singh · Malaya Journal of Matematik · 2020

Showing 3 of 6 known citations — external sources report more than can currently be individually listed.

Article metrics

Real usage data collected on this platform.

24

Page views

0

PDF downloads

2

Outbound clicks

6

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.