Improved Chebyshev–Halley family of methods with seventh and eighth order of convergence for simple roots

Improved Chebyshev–Halley family of methods with seventh and eighth order of convergence for... The principle aim of this manuscript is to introduce a new highly efficient improved modification of Chebyshev–Halley family with increasing order of convergence. The idea is based on the schemes proposed by Li et al. (Appl Math Comput 235:221–225, 2014) and Sharma (Appl Math Comput 256:119–124, 2015). The proposed scheme has at least seventh-order of convergence and also posses an optimal eighth-order of convergence for a particular value of the disposable parameter. Each member of the proposed scheme is free from second-order derivative and requires only four functional evaluations (viz. three evaluations of function f and one of first-order derivative $$f'$$ f ′ ) per full iteration. A variety of concrete numerical examples demonstrates that our proposed scheme performs better than the existing schemes proposed by Li et al. (Appl Math Comput 235:221–225, 2014) and Sharma (Appl Math Comput 256:119–124, 2015). Dynamical study of our methods also confirms the above conclusions to a great extent. Moreover, the local convergence of these methods is given using hypotheses only on the first derivative and Lipschitz constants. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

Improved Chebyshev–Halley family of methods with seventh and eighth order of convergence for simple roots

Loading next page...
 
/lp/springer_journal/improved-chebyshev-halley-family-of-methods-with-seventh-and-eighth-goEDtz1wvN
Publisher
Springer Milan
Copyright
Copyright © 2017 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0106-9
Publisher site
See Article on Publisher Site

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 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

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

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial