New Perspectives in Applied Mathematics with Nonlinear Equations and Dynamical Systems

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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

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.

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