Ms. Paula Triguero-Navarro

Eva García Villalba

Iterative schemes for finding all roots simultaneously of nonlinear equations

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.

16 July 2022 in Applied Mathematics Letters

Journal Article

Alicia Cordero

Neus Garrido

A General Optimal Iterative Scheme with Arbitrary Order of Convergence

16 May 2021 in Symmetry

Journal Article

Design of iterative methods with memory for solving nonlinear systems

A general optimal iterative method, for approximating the solution of nonlinear equations, of

(n + 1)

steps with

2^{n + 1}

order of convergence is presented. Cases

n = 0

and

n = 1

correspond to Newton’s and Ostrowski’s schemes, respectively. The basins of attraction of the proposed schemes on different test functions are analyzed and compared with the corresponding to other known methods. The dynamical planes showing the different symmetries of the basins of attraction of new and known methods are presented. The performance of different methods on some test functions is shown.

12 March 2023 in Mathematical Methods in the Applied Sciences

Journal Article

Neus Garrido

An iterative scheme to obtain multiple solutions simultaneously

In this paper, we design two parametric classes of iterative methods without memory to solve nonlinear systems, whose convergence order is 4 and 7, respectively. From their error equations and to increase the convergence order without performing new functional evaluations, memory is introduced in these families of different forms. That allows us to increase from 4 to 6 the convergence order in the first family and from 7 to 11 in the second one. We perform some numerical experiments with big size systems for confirming the theoretical results and comparing the proposed methods along other known schemes.

3 June 2023 in Applied Mathematics Letters

Journal Article

Neus Garrido

Jacobian‐Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously

12 January 2025 in Mathematical Methods in the Applied Sciences

Journal Article