Applied Research with Two Modified Three-Step Algorithms Based on Double Newton Method for Solving Nonlinear Equations

Liang Fang

doi:10.4028/www.scientific.net/AMR.951.235

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 951Applied Research with Two Modified Three-Step...

Applied Research with Two Modified Three-Step Algorithms Based on Double Newton Method for Solving Nonlinear Equations

Abstract:

With the rapid development and wide application of information engineering and applied technology, nonlinear problems become an important direction of research in the field of numerical calculation and analysis. In this paper, we mainly study the iterative methods of nonlinear equations. We present and analyze two modified three-step Newton-type methods based on double Newton method for solving nonlinear equations. One is sixth-order convergent, while the other is seventh-order convergent. Both methods are free from second derivatives. The efficiency indices of the presented methods are 1.4310 and 1.4758, respectively, both of which are better than that of the classical Newton’s method 1.414. Some numerical experiments illustrate the efficiency and performance of the proposed methods.

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Periodical:

Advanced Materials Research (Volume 951)

Pages:

235-238

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.951.235

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Online since:

May 2014

Authors:

Liang Fang*

Keywords:

Double Newton Method, Efficiency Index, Iterative Method, Newton Method, Nonlinear Equation

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