Dear Colleagues,

Solving nonlinear equations is a problem that appears frequently in different scientific disciplines. It is a well-known fact that the solutions of such equations can rarely be found in closed form, so we need to use iterative procedures to solve them. When talking about iterative procedures, the most well-known, studied, and used one is Newton’s method, due to its good properties related to the convergence and the easy way of computing it. However, sometimes this method cannot be used for solving equations since the computation of the inverse of the derivative can be too costly or even not possible, leading one to consider alternative approaches such as the secant method or other derivative-free methods. On the other hand, sometimes researchers need to use higher-speed and higher-order iterative methods that have been developed for such purposes.

In the study of these iterative procedures, the following fields are of interest:

• Semilocal convergence, in which you should impose conditions on the function involved and the starting point or guess;
• Local convergence, in which you must impose conditions on the solution and the function involved;
• Global convergence, which is the most complicated one to prove;
• Dynamical studies, where fractals appear.

The main target of this Special Issue is to show some research lines developed in this discipline, such as the analysis of the dynamical behavior of nonlinear equations that can allow researchers to find different new ways for finding solutions for these equations. We welcome manuscripts considering areas including (but not limited to) the following:

• Study of real dynamics, by means of using Lyapunov exponents, Feigenbaum diagrams, or other tools such as the convergence plane;
• Study of complex dynamics, by means of using parameter and dynamical planes;
• Comparison of the real and complex dynamics of an iterative method;
• Study of the dynamics of higher-order methods;
• Development of different tools to help researchers in the study of dynamical behavior;
• Comparison of the results obtained in different languages such as MATLAB, Python, C++, and Mathematica.

Prof. Dr. Ángel Alberto Magreñán
Prof. Dr. Iñigo Sarría
Guest Editors

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• iterative methods
• numerical analysis
• semilocal convergence
• dynamical behavior
• fractal
• fractal dimension