✦ LIBER ✦

New eighth-order iterative methods for solving nonlinear equations

✍ Scribed by Xia Wang; Liping Liu

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 310 KB
Volume: 234
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2010.03.002

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✦ Synopsis

a b s t r a c t

In this paper, three new families of eighth-order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods. Per iteration these iterative methods require three evaluations of the function and one evaluation of the first derivative. This implies that the efficiency index of the developed methods is 1.682, which is optimal according to Kung and Traub's conjecture for four function evaluations per iteration. Notice that Bi et al.'s method in [2] and [3] are special cases of the developed families of methods. In this study, several new examples of eighth-order methods with efficiency index 1.682 are provided after the development of each family of methods. Numerical comparisons are made with several other existing methods to show the performance of the presented methods.

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