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

A triparametric family of fourth-order multiple-zero solvers have been proposed. In this paper, we select among them a uniparametric family of optimal fourth-order multiple-zero solvers with rational weight functions and pursue their dynamics by exploring the relevant parameter spaces and dynamical planes, by means of Möbius conjugacy map applied to a prototype polynomial of the form (z-A)m(z-B)m. The resulting dynamics is best illustrated through various stability surfaces and parameter spaces as well as dynamical planes.

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New class of sixth-order nonhomogeneous p(x)-Kirchhoff problems with sign-changing weight functions

Advances in Nonlinear Analysis ◽

10.1515/anona-2020-0172 ◽

2021 ◽

Vol 10 (1) ◽

pp. 1117-1131

Author(s):

Mohamed Karim Hamdani ◽

Nguyen Thanh Chung ◽

Dušan D. Repovš

Keyword(s):

Sixth Order ◽

Weight Functions ◽

New Class

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Development of a Family of Jarratt-Like Sixth-Order Iterative Methods for Solving Nonlinear Systems with Their Basins of Attraction

Algorithms ◽

10.3390/a13110303 ◽

2020 ◽

Vol 13 (11) ◽

pp. 303

Author(s):

Min-Young Lee ◽

Young Ik Kim

Keyword(s):

Nonlinear Systems ◽

Iterative Methods ◽

Basins Of Attraction ◽

Sixth Order ◽

Weight Functions ◽

Computational Studies ◽

Numerical Examples ◽

Convergence Behavior ◽

Global Character ◽

Special Cases

We develop a family of three-step sixth order methods with generic weight functions employed in the second and third sub-steps for solving nonlinear systems. Theoretical and computational studies are of major concern for the convergence behavior with applications to special cases of rational weight functions. A number of numerical examples are illustrated to confirm the convergence behavior of local as well as global character of the proposed and existing methods viewed through the basins of attraction.

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Weight Functions for Short Discrete Fourier Transforms in Radar Systems of Signal Acquisition and Processing

Telecommunications and Radio Engineering ◽

10.1615/telecomradeng.v57.i4.90 ◽

2002 ◽

Vol 57 (4) ◽

pp. 6

Author(s):

Yu. L. Meister ◽

D. M. Pisa

Keyword(s):

Fourier Transforms ◽

Weight Functions ◽

Signal Acquisition ◽

Discrete Fourier Transforms ◽

Radar Systems ◽

Signal Acquisition And Processing

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A Meshless Method Based on the Nonsingular Weight Functions for Elastoplastic Large Deformation Problems

International Journal of Applied Mechanics ◽

10.1142/s1758825119500066 ◽

2019 ◽

Vol 11 (01) ◽

pp. 1950006 ◽

Cited By ~ 46

Author(s):

Fengbin Liu ◽

Qiang Wu ◽

Yumin Cheng

Keyword(s):

Large Deformation ◽

Numerical Solutions ◽

Weak Form ◽

Weight Functions ◽

Computational Accuracy ◽

Lagrange Formulation ◽

Element Free Galerkin ◽

Penalty Factor ◽

Element Free ◽

Large Deformation Problems

In this study, based on a nonsingular weight function, the improved element-free Galerkin (IEFG) method is presented for solving elastoplastic large deformation problems. By using the improved interpolating moving least-squares (IMLS) method to form the approximation function, and using Galerkin weak form based on total Lagrange formulation of elastoplastic large deformation problems to form the discretilized equations, which is solved with the Newton–Raphson iteration method, we obtain the formulae of the IEFG method for elastoplastic large deformation problems. In numerical examples, the influences of the penalty factor, scale parameter of influence domain and weight functions on the computational accuracy are analyzed, and the numerical solutions show that the IEFG method for elastoplastic large deformation problems has higher computational efficiency and accuracy.

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An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.220-223.2585 ◽

2012 ◽

Vol 220-223 ◽

pp. 2585-2588

Author(s):

Zhong Yong Hu ◽

Fang Liang ◽

Lian Zhong Li ◽

Rui Chen

Keyword(s):

Iterative Method ◽

Nonlinear Equations ◽

Newton’S Method ◽

Newton's Method ◽

Efficiency Index ◽

Sixth Order ◽

Type Method ◽

Second Derivatives ◽

Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

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