Some higher-order modifications of Newton's method for solving nonlinear equations

Authors:
YoonMee Ham;Changbum Chun;Sang-Gu Lee
Affiliations:
Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of Korea;Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
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Abstract

In this paper we consider constructing some higher-order modifications of Newton's method for solving nonlinear equations which increase the order of convergence of existing iterative methods by one or two or three units. This construction can be applied to any iteration formula, and per iteration the resulting methods add only one additional function evaluation to increase the order. Some illustrative examples are provided and several numerical results are given to show the performance of the presented methods.