Constructing higher-order methods for obtaining the multiple roots of nonlinear equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Zhou, Xiaojian^1,2  Chen, Xin¹  Song, Yongzhong¹ 

[1] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210046, Peoples R China

[2] Nantong Univ, Sch Sci, Nantong 226007, Peoples R China

关键词: Nonlinear equations;    Iterative method;    Multiple roots;    Convergence order;    Efficiency index;   

DOI  :  10.1016/j.cam.2011.03.014

来源: Elsevier

【 摘 要 】

This paper concentrates on iterative methods for obtaining the multiple roots of nonlinear equations. Using the computer algebra system Mathematica, we construct an iterative scheme and discuss the conditions to obtain fourth-order methods from it. All the presented fourth-order methods require one-function and two-derivative evaluation per iteration, and are optimal higher-order iterative methods for obtaining multiple roots. We present some special methods from the iterative scheme, including some known already. Numerical examples are also given to show their performance. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free