Developing a new family of Newton–Secant method with memory based on a weight function

Developing a new family of Newton–Secant method with memory based on a weight function In this paper, we construct an iterative method with memory based on the Newton–Secants method to solve nonlinear equations. This proposed method has fourth order convergence and costs only three functions evaluation per iteration and without any evaluation of the derivative function. Acceleration of the convergence speed is achieved by an appropriate variation of a free parameter in each step. This self accelerator parameter is estimated using Newtons interpolation polynomial of third degree. The order of convergence is increased from 4 to 5.23 without any extra function evaluation. This method has the efficiency index equal to $$5.23^{\frac{1}{3}}\approx 1.7358$$ 5 . 23 1 3 ≈ 1.7358 . We describe the analysis of the proposed method along with numerical experiments including comparison with the existing methods. Finally, the attraction basins of the proposed method are shown and compared with other existing methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

Developing a new family of Newton–Secant method with memory based on a weight function

Loading next page...
 
/lp/springer_journal/developing-a-new-family-of-newton-secant-method-with-memory-based-on-a-csgFWLBCeZ
Publisher
Springer Milan
Copyright
Copyright © 2016 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0097-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, we construct an iterative method with memory based on the Newton–Secants method to solve nonlinear equations. This proposed method has fourth order convergence and costs only three functions evaluation per iteration and without any evaluation of the derivative function. Acceleration of the convergence speed is achieved by an appropriate variation of a free parameter in each step. This self accelerator parameter is estimated using Newtons interpolation polynomial of third degree. The order of convergence is increased from 4 to 5.23 without any extra function evaluation. This method has the efficiency index equal to $$5.23^{\frac{1}{3}}\approx 1.7358$$ 5 . 23 1 3 ≈ 1.7358 . We describe the analysis of the proposed method along with numerical experiments including comparison with the existing methods. Finally, the attraction basins of the proposed method are shown and compared with other existing methods.

Journal

SeMA JournalSpringer Journals

Published: Oct 27, 2016

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off