Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2748

Full Length Research Paper

Some multistep higher order iterative methods for non-linear equations

Nazir Ahmad Mir
  • Nazir Ahmad Mir
  • Department of Basic Sciences, Riphah International University, I-14 Islamabad, Pakistan.
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Naila Rafiq
  • Naila Rafiq
  • Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
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  •  Received: 06 June 2014
  •  Accepted: 20 August 2014
  •  Published: 15 September 2014

Abstract

We establish here new three and four-step iterative methods of convergence order seven and fourteen to find roots of non-linear equations. The new developed iterative methods are variants of Newton's method that use different approximations of first derivatives in terms of previously known function values, thus improving efficiency indices of the methods. The seventh and fourteenth order iterative methods use four and five function values including one derivative of a function. So, the efficiency indices of these methods are , respectively. Numerical examples are given to show the performance of described methods.

 

Key words:  Non-linear equation, Iterative methods, convergence order, efficiency index.