The members of the Numerical Analysis Laboratory develop numerical methods for the study of evolutionary problems arising in science, engineering, environmental sustainability, and emerging technologies. Our research combines theoretical analysis with efficient computational techniques for the simulation of complex dynamical systems.
A major research line of the laboratory concerns the development and analysis of numerical methods for evolutionary models described by ordinary, delay, partial, fractional, stochastic, and Volterra integro-differential equations.
We investigate numerical methods for evolutionary problems involving ODEs, DDEs, PDEs, FDEs, SDEs, and VIEs, with particular attention to accuracy, stability, efficiency, and long-time reliability.
The models studied in the laboratory arise from a wide range of applications, including natural, technological, environmental, and social processes characterized by complex time evolution.
Our work integrates theoretical numerical analysis with modern computational tools, including parallel computing, machine learning, and data-driven approaches for large-scale dynamical systems.
The laboratory addresses several challenging application areas where evolutionary mathematical models provide an effective framework for analysis, prediction, and decision support.
We study the spread of epidemics and the propagation of information on social networks through dynamical models capable of describing interaction mechanisms, memory effects, and time-dependent behaviors.
Numerical models are developed for electrochemical processes, with applications to electrodeposition in electric batteries and corrosion phenomena, supporting the analysis of performance, durability, and material evolution.
We investigate the evolution of vegetation in arid and semi-arid environments, together with models of interest for environmental sustainability, aimed at understanding resilience, adaptation, and long-term ecological dynamics.
Alongside classical applications, the laboratory also explores innovative mathematical models motivated by next-generation technologies.
We study numerical models for quantum devices, focusing on the simulation of complex dynamical behaviors where high accuracy, structure preservation, and computational efficiency are essential.
Data-driven numerical methods are employed to identify, approximate, and analyze differential models directly from observed data, opening new perspectives for scientific discovery and predictive modeling.
A distinctive feature of the laboratory is the integration of mathematical modeling, numerical analysis, and high-performance computation in a unified framework for complex dynamical systems.
The laboratory develops and applies a wide spectrum of modern numerical and computational techniques for the approximation of differential problems.
We design efficient, stable, and structure-preserving numerical integrators for time-dependent problems, with particular care for the qualitative properties of the continuous model.
For multidimensional PDEs, we employ splitting techniques based on Approximate Matrix Factorization (AMF) and matrix-oriented approaches that enhance computational efficiency and scalability.
We investigate parallel methods for large systems of ODEs and FDEs, exploiting GPUs and MIMD architectures to address demanding simulations in scientific and engineering applications.
PINNs are used to solve differential equations by combining physical constraints and machine learning, offering flexible tools for complex forward and inverse problems.
We employ data-driven techniques such as SINDy to infer governing equations and reduced models from data, supporting interpretable scientific modeling and system identification.
Our methodological research is driven by the goal of connecting advanced numerical analysis with impactful applications in health, environment, materials science, and quantum technologies.