Iterative methods play a significant role in the study of linear or nonlinear phenomena occurring in engineering, physics, economics, social sciences, life sciences, and medicine. In the recent years, the study of the dynamical behavior of the rational operator associated with an iterative method has become a rapidly growing area of research, since the dynamical properties of the rational operator give us important information about the convergence, efficiency, and reliability of the iterative method.

In this issue we will focus on the new trends in the edge between these areas of research: the analysis of iterative methods for solving nonlinear problems and the dynamical study of the associated operators. Although the main aims of the construction of iterative schemes are to get high order of convergence and computational efficiency, their stability is an important subject to be taken into account: the wideness of basins of attraction, the convergence to attracting elements different from the solution, and so on. The dynamical analysis of the iterative methods gives us interesting information about these topics.

We invite researchers to submit original research articles as well as review articles that will stimulate the continuing efforts to combine numerical and dynamical tools for designing, developing, and applying iterative schemes for solving nonlinear problems. We also encourage the authors to include practical applications in their submissions.

Potential topics include, but are not limited to:

• Dynamical analysis of iterative schemes for solving nonlinear equations
• Study of the stability of iterative procedures for solving linear or nonlinear systems
• Dynamical behavior of recurrence relations versus iterative methods with memory
• Matrix equations: iterative approach and stability
• Stability analysis of interval iterative methods for solving nonlinear equations
• Application to engineering and industrial problems
• Fractals in nature and iterative methods