Giovanni Russo

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.

"Tag med p en kulinarisk rejse til Italien med 'Smagsfulde Italien', en kogebog fyldt med autentiske italienske opskrifter, der vil v kke dine smagsl g og transportere dig til Italiens fortryllende kulinariske verden. Giovanni Russo, en passioneret kok med dyb forst else for det italienske madunivers, deler sine hemmeligheder og traditionelle teknikker, der vil forvandle dine m ltider til autentiske italienske festm ltider. I 'Smagsfulde Italien' vil du opleve en bred vifte af l kre retter, der afspejler Italiens kulinariske mangfoldighed og traditioner. Fra saftige pasta- og risotto-retter til smagfulde pizzaer og forf rende dolce-desserter, disse opskrifter vil bringe det autentiske italienske k kken ind i dit eget hjem. Lad dig inspirere af Giovanni Russos lidenskab og ekspertise, mens han deler sin viden om det italienske k kken og de s rlige ingredienser, der g r retterne unikke. Hver opskrift er ledsaget af historier og anekdoter, der udforsker den rige kulturelle baggrund og betydningen af de italienske retter. Forbered dig p at udforske Italiens kulinariske skatte og skabe uforglemmelige smagsoplevelser i dit eget k kken med 'Smagsfulde Italien'. Bliv en mesterkok i autentisk italiensk madlavning og lad dig forf re af den enest ende smag af Italien."

Networks constitute the backbone of complex systems, from the human brain to computer communications, transport infrastructures to online social systems and metabolic reactions to financial markets. Characterising their structure improves our understanding of the physical, biological, economic and social phenomena that shape our world. Rigorous and thorough, this textbook presents a detailed overview of the new theory and methods of network science. Covering algorithms for graph exploration, node ranking and network generation, among others, the book allows students to experiment with network models and real-world data sets, providing them with a deep understanding of the basics of network theory and its practical applications. Systems of growing complexity are examined in detail, challenging students to increase their level of skill. An engaging presentation of the important principles of network science makes this the perfect reference for researchers and undergraduate and graduate students in physics, mathematics, engineering, biology, neuroscience and the social sciences.

This book contains an expanded and smoothed version of lecture notes delivered by the authors at the Advanced School on Numerical Solutions of Partial Di?- ential Equations: New Trends and Applications, which took place at the Centre de Recerca Matem' atica (CRM) in Bellaterra (Barcelona) from November 15th to 22nd, 2007. The book has three parts. The ?rst part, by Silvia Bertoluzza and Silvia Falletta, is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of wr- ing equivalent norms for the scale of Besov spaces allows to write down some new methods. Thesecondpart,byGiovanniRusso,providesanoverviewofthemodern finite-volume and finite-difference shock-capturing schemes for systems of cons- vationandbalancelaws,with emphasisingiving auni?ed viewofsuchschemesby identifying the essential aspects of their construction. In the last part Chi-Wang Shugivesageneralintroductionto thediscontinuousGalerkinmethods forsolving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates. The school that originated these notes was born with the objective of p- viding an opportunity for PhD students, recent PhD doctorates and researchers in general in ?elds of applied mathematics and engineering to catch up with - portant developments in the ?elds and/or to get in touch with state-of-the-art numerical techniques that are not covered in usual courses at graduate level.

The book is divided into three parts, which contain respectively recent results in the kinetic theory of granular gases, kinetic theory of chemically reacting gases, and numerical methods for kinetic systems. Part I is devoted to theoretical aspects of granular gases. Part II presents recent results on modelling of kinetic systems in which molecules can undergo binary collisions in presence of chemical reactions and/or in presence of quantum effects. Part III contains several contributions related to the construction of suitable numerical methods and simulations for granular gases.