A new eighth-order iterative method for solving nonlinear equations

被引：23

作者：

Thukral, R. ^{[1
]}

机构：

[1] Pade Res Ctr, Leeds LS17 5JS, W Yorkshire, England

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 01期

关键词：

Newton method; Newton-type methods; Nonlinear equations; Order of convergence;

D O I：

10.1016/j.amc.2010.05.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present an improvement of the fourth-order Newton-type method for solving a nonlinear equation. The new Newton-type method is shown to converge of the order eight. Per iteration the new method requires three evaluations of the function and one evaluation of its first derivative and therefore the new method has the efficiency index of (4)root 8, which is better than the well known Newton-type methods of lower order. We shall examine the effectiveness of the new eighth-order Newton-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons are made with several other existing methods to show the performance of the presented method. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：222 / 229

页数：8

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