Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems

被引：14

作者：

Cordero, Alicia ^{[1
]}

Villalba, Eva G. ^{[1
]}

Torregrosa, Juan R. ^{[1
]}

Triguero-Navarro, Paula ^{[1
]}

机构：

[1] Univ Politen Valencia, Multidisciplinary Inst Math, Valencia 46022, Spain

来源：

MATHEMATICS | 2021年 / 9卷 / 01期

关键词：

nonlinear system; iterative method; divided difference operator; stability; parameter plane; dynamical plane; DYNAMICS; FAMILY;

D O I：

10.3390/math9010086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A new parametric class of iterative schemes for solving nonlinear systems is designed. The third- or fourth-order convergence, depending on the values of the parameter being proven. The analysis of the dynamical behavior of this class in the context of scalar nonlinear equations is presented. This study gives us important information about the stability and reliability of the members of the family. The numerical results obtained by applying different elements of the family for solving the Hammerstein integral equation and the Fisher's equation confirm the theoretical results.

引用

页码：1 / 18

页数：18

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