This book presents a collection of cutting-edge research contributions from the 2nd Young Researchers Conference on Numerical Aspects of Hyperbolic Balance Laws and Related Problems. It highlights novel advancements in numerical methods, theoretical analysis, and interdisciplinary applications of hyperbolic partial differential equations. Aimed at researchers, graduate students, and professionals in applied mathematics, scientific computing, and engineering, this book explores advanced numerical techniques such as finite volume and finite element methods, high-resolution schemes, stability analysis, and multiscale modeling. Covering a broad spectrum of applications, it extends from classical fields like fluid mechanics, plasma physics, and granular gases to emerging areas in biology and social sciences, including pedestrian and traffic flow, opinion dynamics, and epidemiology. Bridging theory and computation, this volume serves as a valuable reference for those developing and analyzing numerical schemes for complex systems.

Giulia Bertaglia is Assistant Professor of Numerical Analysis at the University of Ferrara. Her research focuses mainly on the development of numerical methods for multiscale hyperbolic systems and kinetic equations, with particular interest toward applications in biomathematics and fluid dynamics. She is an appointed member of the European Mathematical Society Young Academy (2025-2028) and recipient of the 2025 SIMAI Fausto Saleri Prize.

Elisa Iacomini is Assistant Professor of Numerical Analysis at the University of Ferrara. She obtained her PhD at La Sapienza University of Rome and held postdoctoral positions at the University of Mannheim and RWTH Aachen University. Her research focuses on hyperbolic conservation laws, uncertainty quantification and inverse problems, with applications in vehicular traffic, opinion dynamics and epidemiology.