Next Article in Journal
Comparison of Pressure Distribution in Inclined and Parabolic Slider Bearings
Previous Article in Journal
Determination of the Steady State Response of EFEF/VFVF Supported Rectangular Specially Orthotropic Plates
Article Menu

Article Versions

Export Article

Open AccessArticle
Math. Comput. Appl. 2007, 12(2), 117-124; doi:10.3390/mca12020117

Perturbative Derivation and Comparisons of Root-Finding Algorithms with Fourth Order Derivatives

1
Department of Mechanical Engineering, Celal Bayar University Muradiye, Manisa, Turkey
2
Department of Mathematics, Georgetown University, Washington DC
*
Authors to whom correspondence should be addressed.
Published: 1 August 2007
Download PDF [133 KB, uploaded 30 March 2016]

Abstract

Perturbation theory is systematically used to generate root finding algorithms with fourth order derivatives. Depending on the number of correction terms in the perturbation expansion and the number of Taylor expansion terms, different root finding formulas can be generated. Expanding Taylor series up to fourth order derivatives and taking two, three and four correction terms in the perturbation expansions, three different root finding algorithms are derived. The algorithms are contrasted numerically with each other as well as with the Newton-Raphson algorithm. It is found that the quadruple-correction-term algorithm performs better than the others.
Keywords: Root finding algorithms; perturbation theory; Newton-Raphson method Root finding algorithms; perturbation theory; Newton-Raphson method
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Pakdemirli, M.; Boyacı, H.; Yurtsever, H.A. Perturbative Derivation and Comparisons of Root-Finding Algorithms with Fourth Order Derivatives. Math. Comput. Appl. 2007, 12, 117-124.

Show more citation formats Show less citations formats

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top