developing tools for analyzing dynamical systems – since 2017
Department of Mathematics, Computer Science and Physics (DMIF) – University of Udine
The research activities of the CDLab concern the development, analysis, implementation and application of numerical methods for dynamical systems, in particular infinite-dimensional ones on Banach spaces. They typically arise from functional and abstract equations modeling, e.g., population dynamics in the diverse fields of epidemiology, ecology, and biology, as well as control problems in the context of engineering and complex networks, to name just a few.
The research is devoted to classical areas such as the numerical discretization of solutions (time integration and algorithmic stability), but also and mainly to more advanced and direct methods like approximation of spectra and continuation to address challenging issues about stability, bifurcation and chaotic behaviors, in view of robust analysis and parameter uncertainties.
Beyond standard MATLAB-like skills, a continual development towards alternative solutions is pursued, with an eye constantly kept on high performance and friendly usage, in response to the different needs emerging in the frequent scenario of experts in applications dealing with computationally demanding problems, but without a strong knowledge of numerical analysis or scientific computing.
The CDLab aims also at providing support in learning and training in mathematical software to students, colleagues and researchers, at the University of Udine as well as outside and at the international level, also fostering collaboration and fruitful interaction.