Implicit-Explicit Methods for Evolutionary Partial Differential Equations

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.

Sebastiano Boscarino is Associate Professor of Numerical Aanalysis in the Department of Mathematics and Computer Science at the University of Catania, Italy. He has published numerous research papers on IMEX methods and semi-implicit methods for evolutionary partial differential equations and their applications. His research interests include numerical methods for stiff problems, conservation laws, hyperbolic systems with relaxation, kinetic equations, and semi-Lagrangian methods for kinetic equations.

Lorenzo Pareschi is Chair of Applied and Computational Mathematics at the School of Mathematics, Heriot-Watt University, Edinburgh, UK, and Professor of Numerical Analysis, University of Ferrara, Italy. The results of his research activity are reported in more than 200 scientific publications and five books. His research interests cover a wide range of topics in applied and computational mathematics, mostly related to multiscale modeling and numerical methods for phenomena described by nonlinear partial differential equations, in particular, hyperbolic and mean-field/kinetic equations.

Giovanni Russo is Professor of Numerical Analysis in the Department of Mathematics and Computer Science at the University of Catania, Italy. The results of his research activity are reported in more than 150 scientific publications and three books. His research interests include computational fluid dynamics; numerical methods for kinetic equations; evolutionary partial differential equations; IMEX methods; level set methods; crystal growth: multiscale modeling and numerics; and, more recently, structure and dynamics of complex networks.