Three-step iterative methods for numerical solution of systems of nonlinear equations

被引：13

作者：

Dehghan, Mehdi ^{[1
]}

Shirilord, Akbar ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, 424 Hafez Ave, Tehran 15914, Iran

来源：

ENGINEERING WITH COMPUTERS | 2022年 / 38卷 / 02期

关键词：

Systems of nonlinear equations; Convergence order; Efficiency index; Newton's method; PADE-APPROXIMANTS; CONVERGENCE; DERIVATIVES; FORMULAS;

D O I：

10.1007/s00366-020-01072-1

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we introduce seventh- and sixth-order methods for solving the systems of nonlinear equations. The convergence analysis of the proposed methods is provided. The computational efficiency for these methods is 6(1/(3n+2n2)) and 7(1/(4n+2n2)). Computational efficiency of new methods is compared with Newton's method and some other recently published methods. Numerical examples are included to demonstrate the validity and applicability of the methods and comparison is made with the existing results.

引用

页码：1015 / 1028

页数：14

共 42 条

[1] A parameterized multi-step Newton method for solving systems of nonlinear equations [J].

Ahmad, Fayyaz ;

Tohidi, Emran ;

Carrasco, Juan A. .

NUMERICAL ALGORITHMS, 2016, 71 (03) :631-653

[2] Third-order iterative methods under Kantorovich conditions [J].

Amat, S. ;

Busquier, S. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 336 (01) :243-261

[3] Geometric constructions of iterative functions to solve nonlinear equations [J].

Amat, S ;

Busquier, S ;

Gutiérrez, JM .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 157 (01) :197-205

[4]

Amat S., 2004, Sci. Ser. A Math. Sci. (N.S.), V10, P3

[5]

[Anonymous], 2015, APPL MATH

[6]

[Anonymous], 2014, COMPUTER BASED MODEL

[7] An optimization algorithm for solving the rich vehicle routing problem based on Variable Neighborhood Search and Tabu Search metaheuristics [J].

Antonio Sicilia, Juan ;

Quemada, Carlos ;

Royo, Beatriz ;

Escuin, David .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 291 :468-477

[8]

Argyros IK., 2013, NUMERICAL METHODS NO

[9] On the convergence of an optimal fourth-order family of methods and its dynamics [J].

Argyros, Ioannis K. ;

Alberto Magrenan, A. .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 252 :336-346

[10] An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system [J].

Bhrawy, A. H. .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 247 :30-46

← 1 2 3 4 5 →