Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
Autor:
Chand, Prem Bahadur
; Chicharro, Francisco Israel
; Garrido, Neus
; Jain, Pankaj
Fecha:
11/10/2019Palabra clave:
Revista / editorial:
MDPIMathematics
Citación:
Chand, P.B.; Chicharro, F.I.; Garrido, N.; Jain, P. Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications. Mathematics 2019, 7, 942.Tipo de Ítem:
Articulo Revista IndexadaDirección web:
https://www.mdpi.com/2227-7390/7/10/942![Open Access Open Access](/themes/Mirage2/images/reunir/openaccess.png)
Resumen:
In this paper, using the idea of weight functions on the Potra–Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some known methods of the corresponding order. It is proved that the results obtained from the proposed methods are compatible with other methods. The proposed methods are tested on some problems related to engineering and science. Furthermore, applying these methods on quadratic and cubic polynomials, their stability is analyzed by means of their basins of attraction.
Ficheros en el ítem
![icon](/themes/Mirage2/images/reunir/icons/pdf.png)
Este ítem aparece en la(s) siguiente(s) colección(es)
Estadísticas de uso
Año |
2012 |
2013 |
2014 |
2015 |
2016 |
2017 |
2018 |
2019 |
2020 |
2021 |
2022 |
2023 |
2024 |
Vistas |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
37 |
81 |
30 |
36 |
42 |
39 |
Descargas |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
34 |
61 |
16 |
27 |
15 |
10 |
Ítems relacionados
Mostrando ítems relacionados por Título, autor o materia.
-
Stability and applicability of iterative methods with memory
Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 15/03/2019)Based on the third-order Traub’s method, two iterative schemes with memory are introduced. The proper inclusion of accelerating parameters allows the introduction of memory. Therefore, the order of convergence of the ... -
On the improvement of the order of convergence of iterative methods for solving nonlinear systems by means of memory
Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus ; Torregrosa, Juan Ramón (Applied Mathematics Letters, 06/2020)Iterative methods with memory for solving nonlinear systems have been designed. For approximating the accelerating parameters the Kurchatov's divided difference is used as an approximation of the derivative of second order. ... -
Anomalies in the convergence of Traub‐type methods with memory
Chicharro, Francisco Israel ; Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Computational and Mathematical Methods, 06/08/2019)The stability analysis of a new family of iterative methods with memory isintroduced. This family, designed from Traub's method, allows to add memorythrough the introduction of an accelerating parameter. Hence, the speed ...