Results 21 to 30 of about 205,428 (139)
Development of Optimal Iterative Methods with Their Applications and Basins of Attraction
Symmetry, 2022 In this paper, we construct variants of Bawazir’s iterative methods for solving nonlinear equations having simple roots. The proposed methods are two-step and three-step methods, with and without memory.
Waikhom Henarita Chanu +2 more
semanticscholar +2 more sources
Algorithms, 2015 In this paper, a family of Steffensen-type methods of optimal order of convergence with two parameters is constructed by direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub (J. Assoc. Comput. Math.
Quan Zheng, Xin Zhao, Yufeng Liu
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Mathematics, 2019 Based on the Steffensen-type method, we develop fourth-, eighth-, and sixteenth-order algorithms for solving one-variable equations. The new methods are fourth-, eighth-, and sixteenth-order converging and require at each iteration three, four, and five ...
Jian Li +2 more
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One-Point Optimal Family of Multiple Root Solvers of Second-Order
Mathematics, 2019 This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture.
Deepak Kumar +2 more
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A Higher Order Chebyshev-Halley-Type Family of Iterative Methods for Multiple Roots [PDF]
Mathematics, 2019 The aim of this paper is to introduce new high order iterative methods for multiple roots of the nonlinear scalar equation; this is a demanding task in the area of computational mathematics and numerical analysis. Specifically, we present a new Chebyshev&
Ramandeep Behl +3 more
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A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order [PDF]
Journal of Applied Mathematics, 2012 A class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle.
F. Soleymani +2 more
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Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation
Mathematics, 2019 Finding a simple root for a nonlinear equation f ( x ) = 0 , f : I ⊆ R → R has always been of much interest due to its wide applications in many fields of science and engineering.
Moin-ud-Din Junjua +2 more
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Symmetry, 2019 A number of higher order iterative methods with derivative evaluations are developed in literature for computing multiple zeros. However, higher order methods without derivative for multiple zeros are difficult to obtain and hence such methods are rare ...
J. Sharma, Sunil Kumar, I. Argyros
semanticscholar +2 more sources
A new family of optimal fourth-order iterative methods for nonlinear equations
Results in Control and Optimization, 2022 A new two-parameter family of fourth-order iterative methods for the numerical solution of nonlinear equations of the form f(x)=0has been introduced and their convergence analysis have been performed.
Ahmet Yaşar Özban, Bahar Kaya
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Memory in the iterative processes for nonlinear problems
Mathematical Methods in the Applied Sciences, Volume 46, Issue 4, Page 4145-4158, 15 March 2023., 2023 In this paper, we study different ways for introducing memory to a parametric family of optimal two‐step iterative methods. We study the convergence and the stability, by means of real dynamics, of the methods obtained by introducing memory in order to compare them. We also perform several numerical experiments to see how the methods behave.
Alicia Cordero +3 more
wiley +1 more source