Numerical Analysis in Dynamical Systems—Theory, Algorithms and Applications

Dear Colleagues,

Dynamical systems theory serves as the cornerstone for modeling and understanding the evolution of complex phenomena across virtually all scientific disciplines—from celestial mechanics and climate science to neuroscience and engineering control. The fidelity of these models and the insights derived from them are intrinsically tied to the power and sophistication of the numerical methods employed. As dynamical systems grow in complexity, the development of novel, efficient, and theoretically sound computational algorithms becomes paramount. This intersection of numerical analysis and dynamical systems is a vibrant field of research, driving innovation both in mathematical theory and in practical simulation capabilities. This Special Issue is dedicated to showcasing the latest advances in this critical area, fostering a dialog between theoretical underpinnings and groundbreaking applications. 

We are pleased to invite you to submit your original research or comprehensive review articles for this Special Issue. 

This Special Issue aims to compile a cohesive collection of high-quality research that bridges advanced mathematical theory with practical computational challenges in the study of dynamical systems. We seek contributions that push the boundaries of numerical algorithm design, deepen the theoretical analysis of computational methods, or demonstrate transformative applications where numerical simulation provides key scientific or engineering insights. 

The theme is perfectly aligned with journals focusing on applied mathematics, computational science, nonlinear dynamics, and numerical methods. It sits at the core of using computation to solve complex, time-dependent problems, ensuring relevance to a wide audience of mathematicians, scientists, and engineers. The scope is deliberately focused to ensure depth and coherence, targeting specifically the numerical analysis of dynamical systems while being broad enough to encompass a variety of approaches and applications, which will facilitate reaching the target of at least 10 impactful articles suitable for potential publication as a Special Issue collection. 

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

• Design and analysis of advanced numerical integrators (e.g., geometric, symplectic, structure-preserving, and adaptive methods);
• Numerical methods for bifurcation analysis, continuation, and detection of invariant manifolds;
• Computation of dynamical indicators (e.g., Lyapunov exponents, entropy, ergodic averages);
• Data-driven and machine learning approaches for dynamical systems modeling and prediction;
• Multiscale modeling and heterogeneous time-scale integration techniques;
• High-performance computing and algorithmic scalability for large-scale dynamical systems;
• Applications in nonlinear waves, fluid dynamics, celestial mechanics, molecular dynamics, and biological networks. 

Prof. Dr. Hongtao Fan
Dr. Maria Beccar-Varela
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. 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.

• numerical analysis
• dynamical systems
• geometric integration
• structure-preserving algorithms
• numerical bifurcation analysis
• computational dynamics
• time integration
• Hamiltonian systems
• chaotic systems
• multiscale simulation