A new fourth-order family for solving nonlinear problems and its dynamics

Abstract

In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made in order to choose those elements of the family with better conditions of stability. These results are checked by solving the nonlinear system that arises from the partial differential equation of molecular interaction.

Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications

“…Now, using the values from (6), (12), (13), (21), and (22) in (18), the error equation of the method is…”

“…Dynamics of a rational operator give important information about the convergence, efficiency and stability of the iterative methods. During the last few decades, many researchers, e.g., [10][11][12][13][14][15][16] and references therein, study the dynamical behavior of rational operators associated with iterative methods. Furthermore, there is an extensive literature [17][18][19][20][21] to understand and implement further results on the dynamics of rational functions.…”

An optimization algorithm for solving the rich vehicle routing problem based on Variable Neighborhood Search and Tabu Search metaheuristics

“…The objective function (2) states that the distance traveled and number of vehicles should be minimized, M being a sufficiently large constant. (3) ensures that one and only one node can be visited after an order.…”

“…A vast number of problems from Applied Science including engineering can be brought by means of solving a nonlinear equation using mathematical modeling [1][2][3]. One of that problems, in concrete the capillary transport of goods problem, is studied in this paper.…”

Comparing the basins of attraction for Kanwar–Bhatia–Kansal family to the best fourth order method

“…The idea of using basins of attraction was initiated by Stewart [27] and followed by the works of Amat et al [28][29][30], and [31], Scott et al [32], Chun et al [33,40], Magreňán [34], Argyros et al [35], Chicharro et al [37], and Cordero et al [36,38]. The only papers comparing basins of attraction for methods to obtain multiple roots are due to Neta et al [41], Neta and Chun [18], [42], and Chun and Neta [26].…”