Sebastiano Boscarino – författare

Implicit-explicit (IMEX) time discretization methods have proven to be highly effective for the numerical solution of a wide class of evolutionary partial differential equations (PDEs) across various contexts. These methods have become mainstream for solving evolutionary PDEs, particularly in the fields of hyperbolic and kinetic equations.The first book on the subject, Implicit-Explicit Methods for Evolutionary Partial Differential Equations provides an in-depth yet accessible approach. The authors summarize and illustrate the construction, analysis, and application of IMEX methods using examples, test cases, and implementation details; guide readers through the various methods and teach them how to select and use the one most appropriate for their needs; and demonstrate how to identify stiff terms and effectively implement high-order methods in time for a variety of systems of PDEs.Readers interested in learning modern techniques for the effective numerical solution of evolutionary PDEs with multiple time scales will find in this book a unified, compact, and accessible treatment.

This book presents a curated collection of recent research contributions in the field of nonlinear partial differential equations (PDEs), with an emphasis on hyperbolic problems. These equations are essential for modeling  complex physical phenomena such as wave propagation, fluid dynamics, blood flow, and sediment transport. In many real-world applications, the governing equations are not purely hyperbolic but involve intricate interactions with elliptic or parabolic components.As the field advances through theoretical insights and practical needs, this volume captures innovative developments shaping current research. The contributions included here were originally presented at the 10th International Congress on Industrial and Applied Mathematics (ICIAM), held in Tokyo in 2023. They were selected from minisymposia on hyperbolic PDEs and related topics, each organized by leading experts in the field.The chapters in this book reflect a rich diversity of perspectives and approaches, ranging from rigorous mathematical analysis to computational techniques and real-world applications. By bringing together these works, the volume offers a comprehensive snapshot of the state of the art in hyperbolic PDE research, highlighting both foundational insights and emerging trends.Edited by the organizers of the relevant ICIAM 2023 minisymposia, this book serves as a valuable resource for researchers, practitioners, and graduate students interested in the theoretical and applied aspects of nonlinear PDEs. Whether you are exploring the mathematical underpinnings of wave phenomena or developing models for complex systems in science and engineering, this volume provides both inspiration and practical tools to advance your work.