New Perspectives in Applied Mathematics with Nonlinear Equations and Dynamical Systems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 534

Special Issue Editor


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Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de la Paz 123, 26006 Logroño, La Rioja, Spain
Interests: applied mathematics; dynamics; iterative methods
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Special Issue Information

Dear Colleagues,

The resolution of nonlinear equations poses a recurring challenge across various scientific domains. It is widely acknowledged that closed-form solutions for such equations are seldom attainable, necessitating the application of iterative techniques. Among these methods, Newton's method stands out as the most well-known, extensively studied, and frequently employed, owing to its favorable convergence properties and straightforward computational approach. However, there are instances where this method is impractical due to the high computational cost or even impossibility of computing the derivative's inverse. In such cases, alternative approaches like the secant method or derivative-free methods become viable options. Additionally, researchers may require higher-speed and higher-order iterative methods developed for specific applications.

The exploration of these iterative procedures includes several fields of interest:

  1. Semi-local convergence, involving conditions on the function and starting point or guess;
  2. Local convergence, requiring conditions on the solution and the function;
  3. Dynamical behavior;
  4. Optimal iterative schemes.

This Special Issue aims to showcase research developments in this discipline, particularly delving into the analysis of the dynamic behavior of nonlinear equations. Such investigations offer researchers new avenues for finding solutions to these equations or systems of equations. Manuscripts are encouraged in areas such as the following:

  • Explorations of complex dynamics through parameter and dynamical planes;
  • Multi-point iterative methods (with or without memory);
  • Study of the dynamics of higher-order methods;
  • Development of tools aiding researchers in studying dynamical behavior;
  • Optimal-order derivative-free iterative methods.

Prof. Dr. Iñigo Sarría
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • iterative methods
  • numerical analysis
  • semi-local convergence
  • dynamical behavior
  • optimal-order iterative methods
  • higher-order methods

Published Papers (1 paper)

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Research

26 pages, 864 KiB  
Article
A New Optimal Numerical Root-Solver for Solving Systems of Nonlinear Equations Using Local, Semi-Local, and Stability Analysis
by Sania Qureshi, Francisco I. Chicharro, Ioannis K. Argyros, Amanullah Soomro, Jihan Alahmadi and Evren Hincal
Axioms 2024, 13(6), 341; https://doi.org/10.3390/axioms13060341 - 21 May 2024
Viewed by 372
Abstract
This paper introduces an iterative method with a remarkable level of accuracy, namely fourth-order convergence. The method is specifically tailored to meet the optimality condition under the Kung–Traub conjecture by linear combination. This method, with an efficiency index of approximately 1.5874, employs [...] Read more.
This paper introduces an iterative method with a remarkable level of accuracy, namely fourth-order convergence. The method is specifically tailored to meet the optimality condition under the Kung–Traub conjecture by linear combination. This method, with an efficiency index of approximately 1.5874, employs a blend of localized and semi-localized analysis to improve both efficiency and convergence. This study aims to investigate semi-local convergence, dynamical analysis to assess stability and convergence rate, and the use of the proposed solver for systems of nonlinear equations. The results underscore the potential of the proposed method for several applications in polynomiography and other areas of mathematical research. The improved performance of the proposed optimal method is demonstrated with mathematical models taken from many domains, such as physics, mechanics, chemistry, and combustion, to name a few. Full article
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