Results 31 to 40 of about 205,428 (139)
Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself?
Discrete Dynamics in Nature and Society, Volume 2023, Issue 1, 2023., 2023 In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family.
Alicia Cordero +3 more
wiley +1 more source
A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. An extensive convergence analysis is presented to verify the optimal eighth order convergence of the new family.
Saima Akram +5 more
wiley +1 more source
An Optimal Iterative Technique for Multiple Root Finder of Nonlinear Problems
Mathematical and Computational Applications, 2022 In this paper, an optimal higher-order iterative technique to approximate the multiple roots of a nonlinear equation has been presented. The proposed technique has special properties: a two-point method that does not involve any derivatives, has an ...
Ramandeep Behl +3 more
doaj +1 more source
Mathematical methods in the applied sciences, 2023 In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations. The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into memory methods, their efficiency indices are increased.
R. Erfanifar, M. Hajarian, K. Sayevand
semanticscholar +1 more source
Computer‐Based Fuzzy Numerical Method for Solving Engineering and Real‐World Applications
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 The nonlinear equation is a fundamentally important area of study in mathematics, and the numerical solutions of the nonlinear equations are also an important part of it. Fuzzy sets introduced by Zedeh are an extension of classical sets, which have several applications in engineering, medicine, economics, finance, artificial intelligence, decision ...
Naila Rafiq +7 more
wiley +1 more source
Symmetry, 2023 In this paper, we have constructed new families of derivative-free three- and four-parametric methods with and without memory for finding the roots of nonlinear equations.
G. Thangkhenpau +3 more
semanticscholar +1 more source
A multi-point iterative method for solving nonlinear equations with optimal order of convergence [PDF]
Japan journal of industrial and applied mathematics, 2018 In this study, a three-point iterative method for solving nonlinear equations is presented. The purpose is to upgrade a fourth order iterative method by adding one Newton step and using a proportional approximation for last derivative.
M. Salimi +3 more
semanticscholar +2 more sources
Modified Ostrowski's method with eighth-order convergence and high efficiency index
Applied Mathematics Letters, 2010 In this paper, based on Newton’s method, we derive a modified Ostrowski’s method with an eighth-order convergence for solving the simple roots of nonlinear equations by Hermite interpolation methods.
Xia Wang, Liping Liu
semanticscholar +2 more sources
An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros
Mathematics, 2021 In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α
Ramandeep Behl +3 more
doaj +1 more source
A Derivative Free Fourth-Order Optimal Scheme for Applied Science Problems
Mathematics, 2022 We suggest a new and cost-effective iterative scheme for nonlinear equations. The main features of the presented scheme are that it does not involve any derivative in the structure, achieves an optimal convergence of fourth-order factors, has more ...
Ramandeep Behl
doaj +1 more source