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International Journal of Computer Mathematics Volume 93, 2016 - Issue 8
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Original Articles

Efficient two-step derivative-free iterative methods with memory and their dynamics

Xiaofeng WangSchool of Mathematics and Physics, Bohai University, Jinzhou121013, Liaoning, China;College of Sciences, Northeastern University, Shenyang110819, Liaoning, ChinaCorrespondence[email protected]
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,
Tie ZhangCollege of Sciences, Northeastern University, Shenyang110819, Liaoning, ChinaView further author information
&
Yuping QinCollege of Engineering, Bohai University, Jinzhou121013, Liaoning, ChinaView further author information
Pages 1423-1446 | Received 06 Feb 2014, Accepted 26 Apr 2015, Published online: 13 Jul 2015

Citations (19)

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Xiaofeng Wang. (2018) A family of Newton-type iterative methods using some special self-accelerating parameters. International Journal of Computer Mathematics 95:10, pages 2112-2127.
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Articles from other publishers (18)

Shahid Abdullah, Neha Choubey & Suresh Dara. (2023) An efficient two-point iterative method with memory for solving non-linear equations and its dynamics. Journal of Applied Mathematics and Computing 70:1, pages 285-315.
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Alicia Cordero, Beny Neta & Juan R. Torregrosa. (2023) Reasons for stability in the construction of derivative‐free multistep iterative methods. Mathematical Methods in the Applied Sciences.
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Xiaofeng Wang & Wenshuo Li. (2023) Stability Analysis of Simple Root Seeker for Nonlinear Equation. Axioms 12:2, pages 215.
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Alicia Cordero, Neus Garrido, Juan R. Torregrosa & Paula Triguero-Navarro. (2022) Symmetry in the Multidimensional Dynamical Analysis of Iterative Methods with Memory. Symmetry 14:3, pages 442.
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Beatriz Campos, Alicia Cordero, Juan R. Torregrosa & Pura Vindel. (2022) Dynamical analysis of an iterative method with memory on a family of third-degree polynomials. AIMS Mathematics 7:4, pages 6445-6466.
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Young-Hee Geum & Young-Ik Kim. (2021) Computational Geometry of Period-3 Hyperbolic Components in the Mandelbrot Set. Mathematics 9:19, pages 2519.
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Ramandeep Behl, Alicia Cordero, Juan R. Torregrosa & Sonia Bhalla. (2021) A New High-Order Jacobian-Free Iterative Method with Memory for Solving Nonlinear Systems. Mathematics 9:17, pages 2122.
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Yuxi Tao & Xiaofeng Wan. (2020) A Newton Type Iterative Method with Seventh-Order Convergence. Journal of Physics: Conference Series 1648:4, pages 042123.
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Xiaofeng Wang & Qiannan Fan. (2020) A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter. Mathematics 8:4, pages 540.
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Min-Young Lee & Young Ik Kim. (2019) The dynamical analysis of a uniparametric family of three-point optimal eighth-order multiple-root finders under the Möbius conjugacy map on the Riemann sphere. Numerical Algorithms 83:3, pages 1063-1090.
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Xiaofeng Wang. 2020. Cyber Security Intelligence and Analytics. Cyber Security Intelligence and Analytics 821 826 .
Tianbao Liu, Xiwen Qin & Qiuyue Li. (2019) An optimal fourth-order family of modified Cauchy methods for finding solutions of nonlinear equations and their dynamical behavior. Open Mathematics 17:1, pages 1567-1598.
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Young Hee Geum, Young Ik Kim & Á. Alberto Magreñán. (2018) A study of dynamics via Möbius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions. Journal of Computational and Applied Mathematics 344, pages 608-623.
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Xiaofeng Wang. (2018) A new accelerating technique applied to a variant of Cordero–Torregrosa method. Journal of Computational and Applied Mathematics 330, pages 695-709.
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Xiaofeng Wang. (2018) An Ostrowski-type method with memory using a novel self-accelerating parameter. Journal of Computational and Applied Mathematics 330, pages 710-720.
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Min-Young Lee, Young Ik Kim & Á. Alberto Magreñán. (2017) On the dynamics of a triparametric family of optimal fourth-order multiple-zero finders with a weight function of the principal mth root of a function-to function ratio. Applied Mathematics and Computation 315, pages 564-590.
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Ke Ding, Jong Kyu Kim, Qiang Lu & Bin Du. (2017) An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps. Discrete Dynamics in Nature and Society 2017, pages 1-7.
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Young Hee Geum, Young Ik Kim & Á. Alberto Magreñán. (2016) A biparametric extension of King’s fourth-order methods and their dynamics. Applied Mathematics and Computation 282, pages 254-275.
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