An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications

被引：14
|
作者：
Madhu, Kalyanasundaram [1 ]
Babajee, D. K. R. [2 ]
Jayaraman, Jayakumar [1 ]
机构：
[1] Pondicherry Engn Coll, Dept Math, Pondicherry 605014, India
[2] 65 Captain Pontre St, St Croix 11708, Port Louis, Mauritius
来源：
NUMERICAL ALGORITHMS | 2017年 / 74卷 / 02期
关键词：
System of nonlinear equation; Newton's method; Order of convergence; Multi-step method; Frechet derivatives;
D O I：
10.1007/s11075-016-0163-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we have improved the order of the double-step Newton method from four to five using the same number of evaluation of two functions and two first order Fr,chet derivatives for each iteration. The multi-step version requires one more function evaluation for each step. The multi-step version converges with order 3r+5, r >= 1. Numerical experiments are done comparing the new methods with some existing methods. Our methods are also tested on Chandrasekhar's problem and the 2-D Bratu problem to illustrate the applications.
引用
收藏
页码：593 / 607
页数：15
相关论文
共 50 条
  • [31] Predetermining the number of periodic steps in multi-step Newton-like methods for solving equations and systems of equations
    Argyros, I. K.
    Maruster, St.
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 329 : 420 - 431
  • [32] A new multi-step method for solving nonlinear systems with high efficiency indices
    Erfanifar, Raziyeh
    Hajarian, Masoud
    NUMERICAL ALGORITHMS, 2024, 97 (02) : 959 - 984
  • [33] New Multi-Step Iterative Methods for Solving Systems of Nonlinear Equations and Their Application on GNSS Pseudorange Equations
    Madhu, Kalyanasundaram
    Elango, Arul
    Landry, Rene, Jr.
    Al-arydah, Mo'tassem
    SENSORS, 2020, 20 (21) : 1 - 16
  • [34] On the local and semilocal convergence of a parameterized multi-step Newton method
    Amat, S.
    Argyros, I
    Busquier, S.
    Hernandez-Veron, M. A.
    Yanez, D. F.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 376
  • [35] A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations
    Li, Beibei
    Cui, Jingjing
    Huang, Zhengge
    Xie, Xiaofeng
    APPLICATIONS OF MATHEMATICS, 2024, 69 (03) : 311 - 337
  • [36] SOME NEW MULTI-STEP DERIVATIVE-FREE ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS
    Shah, Farooq Ahmed
    Ul Haq, Ehsan
    TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2020, 10 (04): : 951 - 963
  • [37] Multi-step Adomian decomposition method for solving a delayed Chikungunya virus system
    Chamekh, Mourad
    Latrach, Mohamed Ali
    Abed, Yasser
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2025, 37 (04): : 361 - 372
  • [38] ADIABATIC MULTI-STEP SEPARATION METHOD AND ITS APPLICATION TO COUPLED OSCILLATORS
    MAKAREWICZ, J
    THEORETICA CHIMICA ACTA, 1985, 68 (04): : 321 - 334
  • [39] Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: Application to PDEs and ODEs
    Ahmad, Fayyaz
    Tohidi, Emran
    Ullah, Malik Zaka
    Carrasco, Juan A.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (04) : 624 - 636
  • [40] Some Higher Order Newton-Like Methods for Solving System of Nonlinear Equations and Its Applications
    Madhu K.
    Jayaraman J.
    International Journal of Applied and Computational Mathematics, 2017, 3 (3) : 2213 - 2230
12345