Direct Comparison between Two Third Convergence Order Schemes for Solving Equations

被引:2
|
作者
Regmi, Samundra [1 ]
Argyros, Ioannis K. [1 ]
George, Santhosh [2 ]
机构
[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA
[2] Natl Inst Technol Karnataka, Dept Math & Computat Sci, Mangalore 575025, Karnataka, India
来源
SYMMETRY-BASEL | 2020年 / 12卷 / 07期
关键词
banach space; third convergence order schemes; ball convergence; Chebyshev-type scheme; ITERATIVE METHODS; LOCAL CONVERGENCE; NEWTONS METHOD; SYSTEMS; VARIANTS; DYNAMICS; 2-POINT;
D O I
10.3390/sym12071080
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
We provide a comparison between two schemes for solving equations on Banach space. A comparison between same convergence order schemes has been given using numerical examples which can go in favor of either scheme. However, we do not know in advance and under the same set of conditions which scheme has the largest ball of convergence, tighter error bounds or best information on the location of the solution. We present a technique that allows us to achieve this objective. Numerical examples are also given to further justify the theoretical results. Our technique can be used to compare other schemes of the same convergence order.
引用
收藏
页码:1 / 10
页数:10
相关论文
共 50 条
  • [1] On the convergence of a novel seventh convergence order schemes for solving equations
    Samundra Regmi
    Ioannis K. Argyros
    Santhosh George
    Christopher I. Argyros
    The Journal of Analysis, 2022, 30 : 941 - 958
  • [2] On the convergence of a novel seventh convergence order schemes for solving equations
    Regmi, Samundra
    Argyros, Ioannis K.
    George, Santhosh
    Argyros, Christopher, I
    JOURNAL OF ANALYSIS, 2022, 30 (03): : 941 - 958
  • [3] Local convergence comparison between two novel sixth order methods for solving equations
    Argyros, Ioannis K.
    George, Santhosh
    ANNALES UNIVERSITATIS PAEDAGOGICAE CRACOVIENSIS-STUDIA MATHEMATICA, 2019, 18 (01) : 5 - 19
  • [4] Extending the Convergence of Two Similar Sixth Order Schemes for Solving Equations under Generalized Conditions
    Argyros, Ioannis K.
    George, Santhosh
    Argyros, Christopher, I
    CONTEMPORARY MATHEMATICS, 2021, 2 (04): : 246 - 257
  • [5] Local Comparison between Two Ninth Convergence Order Algorithms for Equations
    Regmi, Samundra
    Argyros, Ioannis K.
    George, Santhosh
    ALGORITHMS, 2020, 13 (06)
  • [6] The Order of Convergence of Difference Schemes for Fractional Equations
    Liu, Ru
    Li, Miao
    Piskarev, Sergey
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (06) : 754 - 769
  • [7] Convergence Criteria of Three Step Schemes for Solving Equations
    Regmi, Samundra
    Argyros, Christopher I.
    Argyros, Ioannis K.
    George, Santhosh
    MATHEMATICS, 2021, 9 (23)
  • [8] A New Class of Halley's Method with Third-Order Convergence for Solving Nonlinear Equations
    Barrada, Mohammed
    Ouaissa, Mariya
    Rhazali, Yassine
    Ouaissa, Mariyam
    JOURNAL OF APPLIED MATHEMATICS, 2020, 2020
  • [9] A Third Order Method for Solving Nonlinear Equations
    Parvaneh, Foroud
    Ghanbari, Behzad
    CHIANG MAI JOURNAL OF SCIENCE, 2017, 44 (03): : 1154 - 1162
  • [10] Ball Comparison Between Four Fourth Convergence Order Methods Under the Same Set of Hypotheses for Solving Equations
    Argyros I.K.
    George S.
    International Journal of Applied and Computational Mathematics, 2021, 7 (1)