Enhancing the Convergence Order from p to p+3 in Iterative Methods for Solving Nonlinear Systems of Equations without the Use of Jacobian Matrices

被引：1

作者：

Cordero, Alicia ^{[1
]}

Leonardo-Sepulveda, Miguel A. ^{[2
,3
]}

Torregrosa, Juan R. ^{[1
]}

Vassileva, Maria P. ^{[2
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Camino Vera S-N, Valencia 46022, Spain

[2] Inst Tecnol Santo Domingo INTEC, Area Ciencia Bas & Ambiental, Av Proceres, Santo Domingo 10602, Dominican Rep

[3] Recinto Felix Evaristo Mejia ISFODOSU, Av Caonabo Leonardo Da Vinci, Santo Domingo 10114, Dominican Rep

来源：

MATHEMATICS | 2023年 / 11卷 / 20期

关键词：

iterative methods; nonlinear systems; local convergence; Jacobian-free scheme;

D O I：

10.3390/math11204238

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we present an innovative technique that improves the convergence order of iterative schemes that do not require the evaluation of Jacobian matrices. As far as we know, this is the first technique that allows us the achievement of an increase, from p to p+3 units, in the order of convergence. This is constructed from any Jacobian-free scheme of order p. We conduct comprehensive numerical tests first in academical examples to validate the theoretical results, showing the efficiency and effectiveness of the new Jacobian-free schemes. Then, we apply them on the non-differentiable partial differential equations that models the nutrient diffusion in a biological substrate.

引用

页数：18