文献类型：期刊文献

英文题名：A variant of Steffensen's method of fourth-order convergence and its applications

作者：Liu, Zhongli[1];Zheng, Quan[2];Zhao, Peng[2]

第一作者：刘忠礼

通讯作者：Liu, ZL[1]

机构：[1]Beijing Union Univ, Coll Biochem Engn, Beijing 100023, Peoples R China;[2]N China Univ Technol, Coll Sci, Beijing 100144, Peoples R China

第一机构：北京联合大学生物化学工程学院

通讯机构：[1]corresponding author), Beijing Union Univ, Coll Biochem Engn, Beijing 100023, Peoples R China.|[1141726]北京联合大学生物化学工程学院;[11417]北京联合大学;

年份：2010

卷号：216

期号：7

起止页码：1978-1983

外文期刊名：APPLIED MATHEMATICS AND COMPUTATION

收录：;EI(收录号：20102312993181);Scopus(收录号：2-s2.0-77953152499);WOS:【SCI-EXPANDED(收录号:WOS:000277703300011)】；

基金：The work is supported by the Scientific Research Project of Beijing Union University (No. 2010) and in part by Natural Science Foundation of Beijing (No. 1072009).

语种：英文

外文关键词：Nonlinear equations; Newton's method; Steffensen's method; Derivative free; Fourth-order convergence; ODEs

摘要：In this paper, a variant of Steffensen's method of fourth-order convergence for solving nonlinear equations is suggested. Its error equation and asymptotic convergence constant are proven theoretically and demonstrated numerically. The derivative-free method only uses three evaluations of the function per iteration to achieve fourth-order convergence. Its applications on systems of nonlinear equations and boundary-value problems of nonlinear ODEs are showed as well in the numerical examples. (C) 2010 Elsevier Inc. All rights reserved.