A Six-Order Method for Non-linear Equations to Find Roots

Authors

  • Manoj Kumar Singh Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India
  • Arvind K. Singh Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India

Keywords:

Newton's method, Iteration function, Order of convergence, Function evaluations, Efficiency index

Abstract

In this paper, new variant of Newton's method based on harmonic mean has been discussed and its sixth order
convergence has been established. The method generates a sequence converging to the root with a suitable choice of
initial approximation ????0
. In terms of computational cost, it requires evaluations of only two functions and two first order
derivatives per iteration and the efficiency index of the proposed method is 1.5651. Proposed method has been compared
with some existing methods. Proposed method is free from the evaluation of the second order derivative of the given
function as required in the family of Chebyshev–Halley type methods. The efficiency of the method is verified on a
number of numerical examples.

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Published

2017-09-25

How to Cite

Manoj Kumar Singh, & Arvind K. Singh. (2017). A Six-Order Method for Non-linear Equations to Find Roots. International Journal of Advance Engineering and Research Development (IJAERD), 4(9), 587–591. Retrieved from https://ijaerd.org/index.php/IJAERD/article/view/3722

Issue

Vol. 4 No. 9 (2017): Volume 4 Issue 9 SEPTEMBER 2017

Section

Articles