Some improvements of Jarratt's method with sixth-order convergence

被引：49
|
作者：
Chun, Changbum [1 ]
机构：
[1] Korea Univ Technol & Educ, Sch Liberal Arts, Cheonan 330708, Chungnam, South Korea
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 190卷 / 02期
关键词：
Newton's method; iterative methods; nonlinear equations; order of convergence; Jarratt's method;
D O I：
10.1016/j.amc.2007.02.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a one-parameter family of variants of Jarratt's fourth-order method for solving nonlinear equations. It is shown that the order of convergence of each family member is improved from four to six even though it adds one evaluation of the function at the point iterated by Jarratt's method per iteration. Several numerical examples are given to illustrate the performance of the presented methods. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：1432 / 1437
页数：6
相关论文
共 50 条
  • [41] Adomian decomposition method with Green's function for sixth-order boundary value problems
    Al-Hayani, Waleed
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (06) : 1567 - 1575
  • [42] Reduced cost numerical methods of sixth-order convergence for systems of nonlinear models
    Harmandeep Singh
    Janak Raj Sharma
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022, 116
  • [43] Reduced cost numerical methods of sixth-order convergence for systems of nonlinear models
    Singh, Harmandeep
    Sharma, Janak Raj
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2022, 116 (04)
  • [44] Sixth-order Moller-Plesset perturbation theory - On the convergence of the MPn series
    Cremer, D
    He, Z
    JOURNAL OF PHYSICAL CHEMISTRY, 1996, 100 (15): : 6173 - 6188
  • [45] A mixed finite element method for a sixth-order elliptic problem
    Droniou, Jerome
    Ilyas, Muhammad
    Lamichhane, Bishnu P.
    Wheeler, Glen E.
    IMA JOURNAL OF NUMERICAL ANALYSIS, 2019, 39 (01) : 374 - 397
  • [46] Modified Jarratt Method Without Memory With Twelfth-Order Convergence
    Soleymani, F.
    Babajee, D. K. R.
    Sharifi, M.
    ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2012, 39 (01): : 21 - 34
  • [47] Nontrivial Periodic Solutions to Some Semilinear Sixth-Order Difference Equations
    Long, Yuhua
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [48] Some sixth-order variants of Ostrowski root-finding methods
    Chun, Changbum
    Ham, YoonMee
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (02) : 389 - 394
  • [49] Periodic and homoclinic solutions of some semilinear sixth-order differential equations
    Tersian, S
    Chaparova, J
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 272 (01) : 223 - 239
  • [50] Identities for Ramanujan's sixth-order mock theta functions
    Choi, YS
    QUARTERLY JOURNAL OF MATHEMATICS, 2002, 53 : 147 - 159
12345