Certain improvements of Newton’s method with fourth-order convergence
Abstract
In this paper we present two new schemes, one is third-order and the other is fourth-order.
These are improvements of second-order methods for solving nonlinear equations and are
based on the method of undetermined coefficients. We show that the fourth-order method
is more efficient than the fifth-order method due to Kou et al. [J. Kou, Y. Li, X. Wang, Some
modifications of Newton’s method with fifth-order covergence, J. Comput. Appl. Math., 209
(2007) 146–152]. Numerical examples are given to support that the methods thus obtained
can compete with other iterative methods.
Description
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2009.06.007
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