Fractal Dynamics in High-Order Iterative Methods
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Numerical and Computational Methods".
Deadline for manuscript submissions: 28 February 2027 | Viewed by 123
Special Issue Editors
Interests: fractal dynamics; numerical methods; numerical optimization; high-order iterative
Interests: partial differential equations; numerical analysis; parallel computing; finite elements
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
We encounter many dynamical systems in science and engineering that evolve or vary over time. Most motions and changes observed in real life are inherently nonlinear. The emergence of high-performance computing has opened the way for visualizing and analyzing complex behavior in the field of nonlinear dynamics. Finding analytical or high-order numerical solutions to nonlinear problems enables deeper investigation of system behavior in the dynamical plane, including the identification of stable and unstable orbits. Such studies provide important insight into the structure of the parameter space, the formation and geometry of basins of attraction, and the chaotic nature of dynamical systems, which has applications across numerous and various fields.
Fractal geometry serves as a vital bridge between numerical stability and complex visual topology. In high-order iterative methods, the boundaries of basins of attraction exhibit self-similar fractal structures, providing a rigorous mathematical framework—through Julia and Fatou sets—to quantify sensitivity to initial guesses and chaotic behavior. Understanding these fractal dynamics is essential for diagnosing numerical uncertainty and designing more robust, predictable, and efficient high-order algorithms.
This Special Issue focuses on ongoing studies in the development of high-order convergent numerical methods for solving nonlinear equations and on the continuous progress of complex dynamical research in the complex plane. In particular, contributions that explore iterative algorithms, visualization and characterization of fractal basin structures, stability analysis, and nonlinear and chaotic phenomena in the dynamical plane are strongly encouraged. Submissions that investigate fractal geometry as a tool to understand sensitivity to initial guesses, parameter space exploration, and the design of more robust high-order algorithms are especially welcome. Applications across diverse fields, including Neural Radiance Fields (NeRF), artificial intelligence (AI), and other computational and engineering problems, are also of interest.
We welcome submissions on the following topics (but not limited to):
- Nonlinear equations and multiple-root finding
- Higher-order convergence methods
- Fractal geometry and visualization of basins of attraction
- Parameter space analysis and sensitivity studies
- Dynamical plane behavior and chaotic phenomena
- Applications in AI, NeRF, and other computational methods
Dr. Younghee Geum
Prof. Dr. Beny Neta
Guest Editors
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 250 words) can be sent to the Editorial Office for assessment.
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. Fractal and Fractional 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 2700 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
- nonlinear equation
- higher-order convergence
- parameter space
- dynamical plane
- multiple-root finder
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