A New Three-step Iterative Method for Solving Nonlinear Equations
In this paper, a new three-step iterative method for finding a simple root of the nonlinear equation of f(x) = 0 will be introduced. This method is based on the two-step method of [C. Chun, Y. Ham, Some fourth-order modifications of Newton’s method, Appl. Math. Comput. 197 (2008) 654-658]. The n...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2012-03-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/95 |
| Summary: | In this paper, a new three-step iterative method for finding
a simple root of the nonlinear equation of f(x) = 0 will be introduced.
This method is based on the two-step method of [C. Chun,
Y. Ham, Some fourth-order modifications of Newton’s method, Appl.
Math. Comput. 197 (2008) 654-658]. The new method requires three
evaluations of the function and two of its first-derivative. We will prove
that the order of convergence of the new method and its efficiency index
will respectively be 8, and 1.5157. Some numerical experiments are
given to illustrate the performance of the three-step iterative method. |
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| ISSN: | 1735-8299 1735-8299 |