Certain improvements of Newton's method with fourth-order convergence

被引：15
|
作者：
Chun, Changbum [1 ]
Neta, Beny [2 ]
机构：
[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea
[2] USN, Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 02期
关键词：
Newton's method; Iterative methods; Nonlinear equations; Order of convergence; Method of undetermined coefficients; Root-finding methods; ITERATIVE METHOD; CONSTRUCTION; VARIANTS; FAMILY;
D O I：
10.1016/j.amc.2009.06.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 modi. cations 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. Published by Elsevier Inc.
引用
收藏
页码：821 / 828
页数：8
相关论文
共 50 条
  • [31] Analyzing the Semilocal Convergence of a Fourth-Order Newton-Type Scheme with Novel Majorant and Average Lipschitz Conditions
    J. P. Jaiswal
    Numerical Analysis and Applications, 2024, 17 : 8 - 27
  • [32] Optimal Convergence Analysis of a Mixed Finite Element Method for Fourth-Order Elliptic Problems
    Yan, Yue
    Li, Weijia
    Chen, Wenbin
    Wang, Yanqiu
    COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2018, 24 (02) : 510 - 530
  • [33] Convergence analysis of a monotone method for fourth-order semilinear elliptic boundary value problems
    Wang, YM
    APPLIED MATHEMATICS LETTERS, 2006, 19 (04) : 332 - 339
  • [34] Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces
    Wang, Xiuhua
    Gu, Chuanqing
    Kou, Jisheng
    NUMERICAL ALGORITHMS, 2011, 56 (04) : 497 - 516
  • [35] New iterative method for solving non-linear equations with fourth-order convergence
    Dehghan, Mehdi
    Hajarian, Masoud
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (04) : 834 - 839
  • [36] Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces
    Xiuhua Wang
    Chuanqing Gu
    Jisheng Kou
    Numerical Algorithms, 2011, 56 : 497 - 516
  • [37] ORDER OF CONVERGENCE OF CERTAIN QUASI-NEWTON-METHODS
    SCHULLER, G
    NUMERISCHE MATHEMATIK, 1974, 23 (02) : 181 - 192
  • [38] 98.07 The order of convergence of Newton's Method in special cases
    McNamee, John Michael
    MATHEMATICAL GAZETTE, 2014, 98 (541): : 119 - 120
  • [39] An accelerated version of Newton's method with convergence order √3
    McDougall, Trevor J.
    Wotherspoon, Simon J.
    Barker, Paul M.
    RESULTS IN APPLIED MATHEMATICS, 2019, 4
  • [40] Fourth-order compact finite difference method for fourth-order nonlinear elliptic boundary value problems
    Wang, Yuan-Ming
    Guo, Ben-Yu
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 221 (01) : 76 - 97
12345